Question

It takes a bus 6 hours to take a trip. The train takes only 4 hours to make the same trip. The train travels at a rate of speed that is 25 mph more than the speed of the bus. What is the rate of the bus and the rate of the train? State what x represents, state the equation, and then state the answer.

Answer 1

x represents the trip distance.

x = 300 miles

Rate of bus = 50 mph

Rate of train = 75 mph

Explanation:

Let the trip distance be x miles.

`\because \: speed = (distance)/(time) \\ time \: taken \: by \: bus \: to \: complete \: \\ the \: trip \: = 6 \: hours \\ \therefore \: speed \: of \: bus = (x)/(6) \: mph \\ \\ time \: taken \: by \: train \: to \: complete \: \\ the \: same \: trip \: = 4 \: hours \\ \therefore \: speed \: of \: train = (x)/(4) \: mph \\ \\ \because \: \: speed \: of \: train \\ =speed \: of \: bus \: + 25 \: mph \\ \therefore \: (x)/(4) = (x)/(6) + 25 \\ \\ \therefore \: (x)/(4) - (x)/(6) = 25 \\ \\ \therefore \: (6x - 4x)/(4 * 6) = 25 \\ \\ \therefore \: (2x)/(24) = 25 \\ \\\therefore \: (x)/(12) = 25 \\ \\ \implies \: x = 25 * 12 \\ \implies \: x =300 \: miles \\ \\ rate \: of \: bus = (x)/(6) = (300)/(6) = 50 \: mph\\ \\ rate \: of \: train = (x)/(4) = (300)/(4) = 75 \: mph`