Question

Ayshab walked x miles at 4 mph.

Answer 1

Answer: Ayshab's average speed for the whole journey =  $3\dfrac{3}{11}\text{ mph}$

Step-by-step explanation:

Formula: Speed = $\dfrac{Distance}{Time}$

i.e. Time = $\dfrac{Distance}{Speed}$

If Ayshab walked x miles at 4 mph, then time taken by him = $\dfrac{x}{4}$ hours

If she then walked 2x miles at 3 mph, then time for this period = $\dfrac{2x}{3}$ hours

Average speed = $\dfrac{Total \ distance}{Total\ time}$

$=\dfrac{x+2x}{\dfrac{x}{4}+\dfrac{2x}{3}}\\\\\\=\dfrac{3x}{x(\dfrac{1}{4}+\dfrac{2}{3})}\\\\\\=\dfrac{3}{\dfrac{3+8}{12}}\\\\\\=\dfrac{3\times12}{11}\\\\=\dfrac{36}{11}\\\\=3\dfrac{3}{11}\text{ mph}$

Hence, Ayshab's average speed for the whole journey =  $3\dfrac{3}{11}\text{ mph}$