Question 1202680
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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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<pre>
Let v be the speed of the first car, in kilometers per hour.

Then the speed of the second car is  {{{(3/2)*v}}},  according to the problem.


The travel time of the first car is  {{{135/v}}}  hours.

The travel time of the second car is  {{{135/((3/2)*v)}}} hours, which is the same as  {{{90/v}}}.


The difference of the travel times is 30 + 45 minutes = 75 minutes = {{{75/60}}} hours = {{{5/4}}} hours.


So we write this "time equation"

    {{{135/v}}} - {{{90/v}}} = {{{5/4}}}.


Simplifying left side, we get

    {{{45/v}}} = {{{5/4}}}.


Thus we find

    v = {{{(45*4)/5}}} = 9*4 = 36.


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

         The speed of the second car is  {{{(3/2)*36}}} = 3*18 = 54 km/h.
</pre>

Solved.