find motorcyclist speed

Question

A motorcyclist, travelling at x km/hr has covered a distance in 2.5 hrs. for the same distance, he would have saved 15 minutes if he had increased the speed by 4 km/h. find the value of x

Answer 1

Distance = (Rate)(Time)

Distance at x km/hr = Distance at x+4 km/hr

2.5x = 2.25(x + 4)

2.5x = 2.25x + 9

0.25x = 9

x = 36 km/hr

Answer 2

Rate · Time = Distance

Slower Trip

x · 2.5 = 2.5x

Increase Speed Trip

x+4 · 2.25 = 2.25(x+4)

Note that a decrease of 15 minutes is a decrease of 1/4 hour or 0.25 of an hour.

New time = 2.5 - 0.25 = 2.25

Since the distance traveled for both trips is the same, the following must be true:

Answer 3

Hi Rayan,

For speed, distance and time problems, the formula is:

Distance = (Speed) x (Time),

You can find any of the missing variable by rearranging the above equation.

Since both the distances are the same for two different speeds, therefore:

Distance at x km/hr = Distance at x+4 km/hr

(2.5) x (x) = (2.25) x (x + 4)

2.25 is the 15 mins less time taken to cover than 2.5 hrs

Solving the equations....

2.5x = 2.25x + 9

Therefore,

0.25x = 9

x = 36 km/hr

Hope it helps. Good Luck! :)