SOLUTION: How fast would you have to go to pass a car going 45 mph from 50 ft behind to 50 ft in front in less than 1/8 mile

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Question 1207181: How fast would you have to go to pass a car going 45 mph from 50 ft behind to 50 ft in front in less than 1/8 mile
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
How fast would you have to go to pass a car going 45 mph
from 50 ft behind to 50 ft in front in less than 1/8 mile
~~~~~~~~~~~~~~~~ 

Let v be the speed of your car, which is required to pass another car as described.

Your car should travel 1/8 mile (which is the same as 0.125 mile) in the same time
as the other car will travel 100 ft less distance.


100 ft is  of a mile, or 0.018939394 of a mile.


So, the other car covers the distance (0.125-0.018939394) = 0.106060606 of a mile
in the same time as your car covers 0.125 of a mile.


Thus, we can write this time equation

     = ,


saying that the time is the same for both cars.


From this equation, you get  v =  = 53.03571432 miles per hour.


Rounding to three decimals, the answer is 53.036 miles per hour.


ANSWER.  The speed of your car should be about 53.036 miles per hour (or higher).

Solved.



Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
1/8 of a mile is equal to 660 feet.

45 miles per hour * 5280 = 237600 feet per hour / 3600 = 66 feet per second.

the car traveling at 45 miles per hour is traveling at 66 feet per second.

if you want to start from 50 feet behind that vehicle and end up 50 feet in front of that vehicle, you must be traveling 100 feet more than that vehicle in 660 feet.

the most that vehicle could be traveling is therefore 550 feet while you traveled 660 feet.

at 66 feet per second, that vehicle will travel 560 feet in 560/66 = 8.48484848... seconds.

in that same amount of time, you needed to travel 660 feet.
660 / 8.48484848.... = 77.78571429 feet per second.

that's the minimum speed you need to be traveling in order to start from 50 feet behind the other car and end up 50 feet ahead of that car.

to visualize this, let the other car start at 50 feet and travel 66 feet per second for 8.48484848..... seconds.

that other car will end up at 50 + 8.48484848 * 66 = 610 feet.

you start at 0 and travel at 77.78571429 feet per second for 8.48484848... second = 660 feet.

the other car started at 50 feet and ended up at 610 feet in 8.48484848..... seconds.

you started at 0 feet and ended up at 660 feet in 8.48484848..... seconds.

you started 50 feet behind the other car and ended up 50 feet ahead of the other car in the same amount of time and you traveled 660 feet to do it.

77.78571429 feet per second is the slowest you can travel to start 50 feet behind and end up 50 feet ahead within 660 feet, which is 1/8 of a mile.

if you travel faster than 77.78571429 feet per second, then you will be able to start 50 feet behind and end up 50 feet ahead in less than 1/8 of a mile.

77.78571429 feet per second * 3600 / 5280 = 53.03571429 miles per hour.

i've check my answer several times and am pretty sure it's correct.

let me know if you agree or if you have any further questions.

theo
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