SOLUTION: Two cars start at a given time and travel in the same direction at average speeds of 40 kph and 55 kph. How much time will elapse before the two cars are 10 km apart?

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Question 1203173: Two cars start at a given time and travel in the same direction at average speeds of 40 kph and 55 kph. How much time will elapse before the two cars are 10 km apart?
Answer by ikleyn(52802) About Me  (Show Source):
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                Physics solution 

Their relative speed is 55 - 40 = 15 kilometers per hour.

In other words, the distance between them is 15*t kilometers, as a function of time.


The cars will be 10 km apart in  10%2F15 = 2%2F3 of an hour,  or in 40 minutes.    ANSWER


                Algebra solution 


Fast car distance from the start is  d%5Bfast%5D = 55*t kilometers.

Slow car distance from the start is  d%5Bslow%5D = 40*t kilometers.


The distance between the cars

    d%5Bfast%5D - d%5Bslow%5D = 55t - 40t.


The distance equation

    55t - 40 t = 10  kilometers.


Simplify and find t

       15t     = 10

         t     = 10%2F15 = 2%2F3 of an hour = 40 minutes.


The same answer.

Solved.

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    - Travel and Distance problems for two bodies moving in opposite directions
    - Travel and Distance problems for two bodies moving in the same direction (catching up)
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