# Question 9de8c

Apr 17, 2016

Average speed, $v = \frac{d}{t} = \frac{2 x}{\frac{3 x}{4}} = \frac{8}{3} = 2.67 k m . h {r}^{- 1}$

#### Explanation:

Define the distance of A to B as x.

Average speed is total distance divided by total time taken. We already know that since the man walks from A to B and then B to A he travelled a distance of 2x. All we need to calculate is the total time taken.

Calculate the times taken.
A to B: v = d/t ⇒ t_1 = d_1/v_1 = x / 2#
B to A: ${t}_{2} = {d}_{2} / {v}_{2} = \frac{x}{4}$

Calculate total time and then average speed.
Total time taken, $t = {t}_{1} + {t}_{2} = \frac{x}{2} + \frac{x}{4} = \frac{3 x}{4}$

Average speed, $v = \frac{d}{t} = \frac{2 x}{\frac{3 x}{4}} = \frac{8}{3} = 2.67 k m . h {r}^{- 1}$