SOLUTION: Two cars left a station in Bawku and were travelling to Tamale a distance of 135km away. The second car left 30 minutes after the first car had left. If the speed of the second car

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Question 1202680: Two cars left a station in Bawku and were travelling to Tamale a distance of 135km away. The second car left 30 minutes after the first car had left. If the speed of the second car is 3/2 times as fast as the first car, and the second car got to Tamale 45 minutes before the first car arrived
Calculated the speed of each car

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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Two cars left a station in Bawku and were travelling to Tamale a distance of 135km away.
The second car left 30 minutes after the first car had left.
If the speed of the second car is 3/2 times as fast as the first car,
and the second car got to Tamale 45 minutes before the first car arrived,
calculated the speed of each car.
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Let v be the speed of the first car, in kilometers per hour.

Then the speed of the second car is  %283%2F2%29%2Av,  according to the problem.


The travel time of the first car is  135%2Fv  hours.

The travel time of the second car is  135%2F%28%283%2F2%29%2Av%29 hours, which is the same as  90%2Fv.


The difference of the travel times is 30 + 45 minutes = 75 minutes = 75%2F60 hours = 5%2F4 hours.


So we write this "time equation"

    135%2Fv - 90%2Fv = 5%2F4.


Simplifying left side, we get

    45%2Fv = 5%2F4.


Thus we find

    v = %2845%2A4%29%2F5 = 9*4 = 36.


ANSWER.  The speed of the first car is  36 km/h.

         The speed of the second car is  %283%2F2%29%2A36 = 3*18 = 54 km/h.

Solved.