So there's been a major fire, car crash, robbery, heart attack, or other catastrophe. Isn't it amazing how the police, firefighters, or EMTs show up really quickly, often in a matter of seconds? Sometimes, you don't even have to call 911!
If only it worked like that in Real Life. It usually takes around 10 minutes for the emergency responders to arrive, and even then, it often takes a while before they can actually do anything. For example, when firefighters arrive at a fire, it usually takes around 5 minutes from the time of arrival before they can actually start spraying water on the fire. This is one of the reasons why real estate near major hospitals is so expensive: you get a much quicker reaction time, obviously. It's also why living next to a fire station makes your homeowner's or renter's insurance far lower at least for fire coverage, and unlike in the hospital example, fire station real estate generally doesn't cost more in money - due to the (in urban areas) near-continual noise.
Note: Cases where it's explicitly mentioned that an ambulance or fire truck simply happened to be nearby (known to emergency responders as a "running call") fit better under Contrived Coincidence.
Compare/contrast Ambulance Cut, where there's a quick cut from the emergency to the response, usually for laughs.
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Those home security system commercials will often show a frantic homeowner calling for help (for example, if a robber is breaking in), and the security center workers dispatching police, who arrive seconds later, to heroically save the homeowner. In Real Life, these things create so many false alarms that alarm companies are usually required to telephone the homeowner and find out if they're at home before alerting the emergency services, unless in cases like personal panic alarms or commercial fire alarms.
Averted for laughs in a Jimmy Johns commercial. A man calls Jimmy Johns to deliver a sandwich and the delivery boy discovers the customer's house is on fire. The customer called Jimmy Johns because he knew they'd get there quickly and he needed help putting out the fire. He then proceeds to call five more delivery guys who all show up before the fire department. The customer called the fire department before calling anyone at Jimmy Johns.
Inverted in the case of most Filipino action films. The Tragic Hero usually has enough time for an elaborate pre-death speech before the cops / paramedics / what-have-you arrive. And usually, when they finally arrive, the hero has already passed on.
Notably averted in Iron Man 2, where it takes several minutes for a SWAT team to respond to Vanko's attack on the Monaco racing event.
Averted in Heat: During the armored car robbery, Neil's crew calculates an estimated police response time of three minutes from the moment they begin the robbery, and they just narrowly manage to fit the robbery into that time window.
Averted in Clerks II. Dante calls the firemen thinking the Mooby's is on fire, but it's the smoke machine from the donkey show Randall has gotten as a going away present. They take so long Dante forgets calling them.
Heavily parodied in Last Action Hero. When our villain first enters the Real World, he's shocked to discover that you can steal a car without sirens instantly sounding. To test this new situation, he walks up to a man and shoots him in the head, then waits for the sirens. When that doesn't work, he yells that he's just shot and killed a man, to which the only response is someone off-screen yelling to quit making a racket.
Averted and used as a major plot point in Reservoir Dogs when Mr. Pink explains to Mr. White how the police arrived at their heist far too soon to have been responding to the alarm. This discrepancy is what convinces Mr. Pink that one of their party is The Mole.
It takes only moments for the police to show up after the main character in American History X kills a would-be thief outside his house.
In fairness the robbery had been going on for a few minutes prior.
A particularly bad straight example happens in the movie A Bronx Tale. 8 year old Calogero observes the neighborhood mobster that he idolizes intervene in a fight that had gotten out of hand by shooting the attacker. His mother whisks him upstairs and into their apartment, and within seconds of them shutting the door the police are knocking on it. Later in the film, a group of young Italian thugs attack a group of black students biking through their neighborhood, within about a minute people are shouting for them to leave because they can already see and hear the sirens coming. Given that both NYPD response time and the unlikeliness of getting an answer when trying to directly call a police precinct has been a source of controversy/outrage in New York for decades, this break from reality seems egregious.
In the first Superman movie, the police, fire trucks, and camera crews all show up within seconds of Lois Lane's helicopter crash. Not sure why they bothered, though, since they couldn't even keep people off the sidewalk in front of the building (where the helicopter was going to hit when it fell seconds later.)
Implied in The Room. A couple minutes after Johnny has committed suicide, emergency lights can be seen flashing in the background, before anyone could even have had a chance to call for emergency responders.
Lampshaded and Subverted in Phone Booth. The main character Stu, who's being held hostage in a phone booth in busy New York city by a hidden sniper, warns the sniper that if he fires his gun, there'll be absolute chaos and cops swarming all over. The sniper decides to test this by shooting a nearby toy robot, and then mocks Stu when nobody even notices.
Live Action TV
Lampshaded in the (unaired) Dollhouse pilot. A police car shows up almost immediately after Assassin!Echo shoots Paul Ballard prompting Echo to remark such a quick response time is unlikely.
Averted in one episode of Law & Order: SVU when Olivia gets into a car accident with Elliot's (pregnant) wife, who goes into labor and has to be extracted from the car. It takes several minutes for the emergency response to arrive and an even longer time for her to actually be extracted. The show does play this straight at other times, though.
Averted in the Buffy the Vampire Slayer episode "The Body". Not only does the ambulance take a long time to arrive, but the sorrow of a relative of the eponymous 'body' is shown entirely during those long, long minutes.
Those Thunderbirds are extraordinarily fast—the situation has barely had time to decay when they arrive. Which is all the more amazing when you consider that they're operating from an island in the middle of the South Pacific Ocean.
Averted in the Firefly episode "Trash," when Haymer activates his own personal panic alarm. It takes about ten minutes or so in real-time for police to arrive, during which time he's quietly stalling Mal and Saffron.
While response times were narrowed for obvious dramatic and show-length reasons, Emergency! did generally avert instant response by indicating several minutes or more had passed between alarm and arrival (in fact, every dispatch would end with an ETA, rarely under 10 minutes, often more). One episode which had a subplot of paramedics being pissed off because they were being called out to dinky non-emergencies had them commenting about the length of time it was taking units to arrive on a scene because the closest unit that should have responded was off on one of the the crap calls. This is, unfortunately, Truth in Television. People call 911 (or their equivalent emergency number) for non-emergency medical situations The consequence is that fewer fire/EMS units are left available for other true emergencies, such as car accidents, heart attacks, etc, and have to respond from a greater distance, increasing response times.
Happens in an episode of Kamen Rider Black, as an ambulance responds immediately to a car accident. The main characters find this odd because no police arrived on the scene, nor had anyone called for help. It turns out to be part of a Golgom plot to "recruit" people for the ultimate terrorist army.
Averted in an episode of 7th Heaven when Julie goes into labor at the Camden House the family calls for an ambulance but it doesn't arrive until well after the baby is born.
Deconstructed at least twice in Burn Notice. On one occasion, Michael's voiceover explains that to get the police to respond on your schedule, you have to call ahead. Mike's preferred method is to report a few minor crimes in a five-block radius.
A bizarre example happens in Boy Meets World, where Eric accidentally sets a curtain on fire, and firefighters appear instantaneously, gratuitously hacking through the (unlocked) door with an ax.
An aversion of this to the first break in the "Child Predator" case in Elementary. The kidnapper panicked and fled hastily (Leaving behind a clue) because he heard a police siren and thought they were after him, despite the fact that there hadn't been enough time for his crime to have even been noticed, much less reported. The police were actually responding to an unrelated call made at a residence a couple blocks away.
Averted in Rescue911 considering that the true stories having emergency services seeming to take forever to get to the emergencies. For instance, there is a story of wounded man in an isolated farm house and it was noted that it would take 20 minutes for the ambulance to get there at maximum speed with lights and siren.
Played for laughs in Robert Rankin's The Antipope: "The fire brigade, who arrived in record time, on hearing it was a pub on fire.."
Discussed in The Dresden Files; police response time varies to the various magical incidents around Chicago. An attack by a group of fear-feeding fae fiends on a major convention gets a swift response, while a couple of wizards duking it out in the streets of a low-income commercial area in the middle of the night takes a few minutes for the police to arrive. When a particularly brutal blizzard hits the Windy City in Small Favor, police and fire response is slowed to a crawl, enabling Harry to get away cleanly, if coldly, from several major supernatural throwdowns well before the police arrive.
In Cyberpunk 2020, the Trauma Team arrives after a random number of minutes. Usually pretty darn quick, as it is determined by d10 roll (and thus, 10 minutes is longest they can take), but this is justified as they fly in VTOL aircrafts and are not hindered by traffic - or buildings, for that matter.
Averted in most RPGs, usually Dungeons & Dragons, where the town guard never shows up until a fight has ended.
Unless your DM wants you to stay on the tracks, then the guards show up instantly when an unscripted fight starts.
The DocWagon contract paramedics of Shadowrun are guaranteed to show up within ten minutes or their immediate treatment is free. There is no general reason to expect them much faster, though.
In the d20 Modern supplement Urban Arcana, the "City Districts" section of the book details the average expected response time for emergency services in each district of a typical city. They range from near-instant (less than one minute for high-security areas like airports and seaports) nearly-immediate (<5 minutes for affluent business or residential areas) to average (5-15 minutes for middle-class residential or business areas or industrial zones) lengthy (15-30 minutes in lower-class areas, rural areas, and industrial zones) to very lengthy (At least half an hour to an hour for underground areas, subways, and sewer systems).
Parodied in Futurama, during the wedding between a Gender Bendered Bender and Calculon. When "Coilette" is supposedly wounded, Zoidberg appears before Calculon is even finished calling for a doctor, complete with obligatory "I came as soon as I could." Justified in that the whole thing was staged.
Lampshaded in Regular Show, after Benson blows up the Party Pete clone along with the party company the police automatically shows up.
Police: We came when we saw the explosion. Rigby: You guys got here fast. Police: Of course we did we're the police.
While the trope is not to be expected in most cases in Real Life, there are some generalized situations where it can exist, or at least usual times can be sped up.
For quick medical response, generally real estate nearest hospitals or fire stations (in places that have EMS as part of the fire service) will have a far faster response time, as will areas close to where paramedics generally take meals or frequently respond to other calls. Also, some events will have paramedics or firefighters on standby - you have a far better chance of immediate help or treatment at such an event then at one where they need to be called.
For quick fire response, being near a fire station and within the first five floors of a building is the best, with being near areas where on-duty firefighters stop for meals next. For quick brush fire response, your place is a lot safer if it's near a reservoir, lake, ocean, large river, or even very large pool as firefighters working via helicopter tend to set up near sources of available water, and helicopter/aircraft drops are the most likely to put out large areas of fire.
For quick police response, being near a police station, near a highly-patrolled area, a gun range (since many cops will go to other ranges as well as the official police range, if there is even a police range) or near where the cops tend to hang out is best, though it may put you at risk if you personally do something stupid that turns out to be illegal. If you wish to protect yourself from random street crime such as robbery or theft, do your work on electronic devices/count money/similar at coffee shops or donut shops frequented by cops - few thieves are stupid enough to steal anything from anyone where there's a police cruiser parked outside. This is also why, if you work the graveyard shift at a gas station or convenience store, it's a good idea to make friends with some guys in blue if you can - having police regularly visiting your store at those hours for snacks or drinks or to fuel up the patrol car or whatever makes it a less appealing target for robbery.