SOLUTION: 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?

Let "x" be the train speed, in km/h.

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

The train covers 1500 km in  hours.

The bus does it in  hours.

The condition  says

 -  = 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,

 =  = .

Only positive root makes sense: x =  = 125.

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

Answer.  How long will it take for the train to travel the 1500 km? -  = 12 hours.

Let time train takes to travel 1,500 miles be T

Then time bus takes is: T + 3

Speed of train = , and speed of bus = 

We then get the following SPEED equation: 

1,500(T + 3) = 1,500T + 25T(T + 3) ------ Multiplying by LCD, T(T + 3) 











(T - 12)(T + 15) = 0 

T, or time train takes =         OR         T = - 15 (ignore)