Question 1054464
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The average speed of an express train is 40 km/hr faster than the average speed of a bus. 
To travel 1200 km,the bus requires 50% more time than the train. Determine the average speed of the bus and the train.
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<pre>
Let x = the bus speed, in {{{km/h}}}.
Then the train speed is (x+40) {{{km/h}}}.

The time for the bus to cover 1200 km is {{{1200/x}}}.
The time for the train is {{{1200/(x+40)}}}.

We are given that

{{{1.5*(1200/(x+40))}}} = {{{1200/x}}}.

Cancel the factor 1200 in both sides. You will get

{{{1.5/(x+40)}}} = {{{1/x}}}.

Multiply both sides by x*(x+40). You will get

1.5x = x+40  --->  0.5x = 40  --->  x = {{{40/0.5}}} = 80 {{{km/h}}}.

It is the bus speed. Then the trai speed is 40 {{{km/h}}} more, i.e. 120 {{{km/h}}}.

<U>Answer</U>.  The train speed is 120 km/h.  The bus speed is 80 km/h.
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