Question

A group of friends go on a 3-hr bike ride together. They ride 15 km with the wind at their backs

and then 15 km straight into the wind. The wind adds or subtracts 3 km/hr from their speed.
Calculate the average speed of the group of friends with no wind.

Answer 1

10.8 km/h to the nearest tenth.

Explanation:

Let x be the average with no wind.

Speed = distance / time

With the wind:

x + 3 = 15 / t A where t = time in hours for the first half of journey

Against the wind:

x - 3 = 15/(3 - t) B

Subtract A - B:

6 = 15/t - 15(3 - t)

6t(3 - t) = 15(3 - t) - 15t

18t - 6t^2 = 45 - 30t

6t^2 - 48t + 45 = 0

2t^2 - 16t + 15 = 0

t = - 1.085

So average speed (from equation B)

x = 15/ (3 - 1.085) + 3

= 10.8 km/h to the nearest tenth.

Answer 2

Explanation:

7km/hr and 13km/hr

Because in this case we divide the total time taken will be 10km/hr but according to the question we have to subtract 3km/hr and also have to add 3km/hr. There for there for there average speed of friends with wind was 7km/hr and friends without wind will be 13km/hr.