Question 1060817
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A train travels 25 km/h faster than a bus. The train takes 3 hours less then the bus to travel 1500 km. 
How long will it take for the train to travel the 1500 km?
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<pre>
Let "x" be the train speed, in km/h.

Then the bus speed is (x-25) km/h.

The train covers 1500 km in {{{1500/x}}} hours.

The bus does it in {{{1500/(x-25)}}} hours.

The condition  says

{{{1500/(x-25)}}} - {{{1500/x}}} = 3.

Multiply both sides by x*(x-25). You will get

1500 x - 1500(x-25) = 3x(x-25),

3x^2 - 75x - 37500 = 0,

x^2 - 25x - 12500 = 0,

{{{x[1,2]}}} = {{{(25 +- sqrt(25^2 +4*12500))/2}}} = {{{(25 +- 225)/2}}}.

Only positive root makes sense: x = {{{250/2}}} = 125.

Thus you found that the train speed is 125 km/h.
Then the bus speed is 125-25 = 100 km/h.

<U>Answer</U>.  How long will it take for the train to travel the 1500 km? - {{{1500/125}}} = 12 hours.
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