Split - Algebra question involving motion. - car

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Mick O'Kelley

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I am just wondering how you would solve this sort of problem? I am stumped a bit by it...

If Car A is traveling at 55 mph -- with Car B traveling behind in the same direction -- how fast would Car B have to travel to catch up to Car A within a distance of 1 mile?

I am perplexed, because it would seem Car B would have to be traveling at an extremely high rate of speed to catch up to Car A in that short of a distance.
 
How far behind car A is car B. Is car B going at a constant speed? This information is quite important!

If car B is just a few feet behind car A then car B can travel just over 55 mph to catch up to car A. On the other hand if car B is a mile behind car A then car B would have to travel quite fast to catch up car A in 1 mile.
 
Suppose car B is x miles behind car A who is traveling at the rate of 55mph. Car B has to travel x+1 miles in the same time as car A travel 1 mile.

Car A: 1 mile = 1 mile(60 minutes/55miles) = (12/11) minutes. That is it will take Car A (12/11)minutes to go 1 mile.

Car B has to go (x+1) miles in (12/11)minutes= (1/55)hrs. So car B has (x+1)miles per (1/55)hours or 55(x+1) miles per hour

So car B has to go at the rate of 55(x+1) miles per hour in order to catch up to car A in 1 miles.

Note that if x is small, then 55(x+1) miles per hour is about 55 miles per hour. If x is large then 55(x+1) miles per hour will be a much faster speed than 55 mph.
 
Jomo said:
How far behind car A is car B. Is car B going at a constant speed? This information is quite important!

Sorry -- my bad! But thank you very much for your efforts. Let me try it another way. Once I have the answer, I can extrapolate.

Car A is doing 55 mph. Car B is traveling at an unknown speed -- a quarter mile behind Car A.

Yet Car B catches up to Car A in a very short time -- about 16 seconds.

In that 16 seconds, Car A would have traveled a quarter mile -- or 1320 feet.

(At 55 mph you travel 80.7 feet per second. 80.7 x 16 = 1291 feet -- just short of a quarter mile.)

In that same 16 seconds, Car B would have to travel .5 miles -- or 2640 feet -- to catch up to Car A.

(Car B had to make up the quarter mile lead -- as well as the quarter mile Car A just traveled.)

To travel 2640 feet in 16 seconds -- Car B would have to be traveling at 105 mph.

At 105 mph you travel 154 feet per second. (154 x 16 = 2464 feet -- just short of a half mile.)

So would I be right in assuming Car B was traveling at 105 mph?

THANK YOU SO MUCH!!!

Mick

Source:

Miles Per Hour to Feet Per Second | Kyle's Converter

Instantly Convert Miles Per Hour (mph) to Feet Per Second (fps) and Many More Speed Or Velocity Conversions Online. Miles Per Hour Conversion Charts. Many Other Conversions.
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There are 5280 feet in a mile -- 1320 feet in a quarter mile. So it would take Car A about 16 seconds to cover a quarter mile.

By the time Car A traveled this quarter mile -- Car B had caught up -- from a starting point about a mile away.

So Car A traveled 1/4 mile at 55 mph which took 16 seconds or so. Car B traveled a mile and a quarter in the same 16 seconds
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