Going against the wind, a cyclist was able to reach 60 km in a matter of 4 hours. With the wind, she was able to cover 150 km in 6 hours.

Question

Going against the wind, a cyclist was able to reach 60 km in a matter of 4 hours. With the wind, she was able to cover 150 km in 6 hours. What would be the speed of the cyclist in calm air and how fast was the wind blowing?

Answer 1

Let r = speed of bicyclist

Let w = windspeed

 

Against the wind:

Rate = r-w = 60/4 = 15 km/hr

 

With the wind:

Rate = r+w = 150/6 = 25 km/hr

 

The speed of the cyclist is the average

(15+25)/2 = 20 km/hr

 

The windspeed is 5 km/hr as can be seen

from r+w = 25   and   r-w = 15