#### Answer

(a) average speed = 48.1 mph
(b) average speed = 50 mph

#### Work Step by Step

(a) $t_1 = \frac{d}{v} = \frac{50~mi}{40~mph}$
$t_1 = 1.25~hours$
$t_2 = \frac{d}{v} = \frac{50~mi}{60~mph}$
$t_2 = 0.833~hours$
total time = $t_1+t_2$
total time = $1.25~h+0.833~h$
total time = $2.08~hours$
average speed = $\frac{100~mi}{2.08~hours}$
average speed = 48.1 mph
(b) Let $t$ be the time spent driving at each speed.
total distance = $40t+60t$
total time = $2t$
average speed = $\frac{40t+60t}{2t}$
average speed = 50 mph