How many minutes will the cyclist have travelled before being being over taken by the motorcyclist?

Question

A cyclist travels at an average speed of 16km/h along a road. 15 minutes after the cyclist sets out, a motorcyclist starting from the same place travels along the same road at an average speed of 48km/h. How many minutes will the cyclist have travelled before being being over taken by the motorcyclist?

please explain how it is done! Thanks !!

Answer 1

Distance = rate*time

d = rt

 

Letting t = time for the cyclist in hours:

 

Bicyclist:  d = 16t

 

The motorcyclist will have driven for 15 minutes less time or t-15 mins.

Putting all times in hours, 15 mins less time is (t - 1/4) hours or (t-0.25) hours:

Motorcyclist:  d = 48(t-0.25)

   

We want to know when the distances travelled will be equal so set the equations

equal to each other and solve for t

 

16t = 48(t-0.25)

16t = 48t -12

-32t = -12

t = -12/(-32) = 3/8 hours

 

(3/8 hours)(60 min/hour) = 22.5 minutes

 

The bicyclist will have travelled for 22.5 minutes

The motorcyclist will have travelled 7.5 minutes