Time and distance problem.

Question

A person travelled 240 km by train ,80 km by car and 125km by bus.Total time for journey was 11 hours. If the speed of the train is 150% the speed of the car and the speed of the bus is 62.5% the speed of the car what is the speed of the bus.?

Please provide the conventional way doing the question and also provide shortcut method

Answer 1

c = speed of car

0.625c = speed of bus

(1.5)(0.625)c = speed of train

 

t = d / r

 

240 / 0.9375c = time of the train

80 / c = time for the car

125 / 0.625c = time for bus

 

240 / 0.9375c + 80 / c + 125 / 0.625c = 11    Multiply both sides by "c"

240/0.9375 + 80 + 125/0.625 = 11c

256 + 80 + 200 = 11c

536 = 11c

 

Up to here the numbers come out neatly. Is "11" the correct number of hours?

 

What do you mean my "conventional" and "short-cut?"