The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 40 miles per hour in 45 minutes, how fast must it travel to cover the same distance in 20 minutes?
A) $\frac{45}{2} \mathrm{mph}$
B) $90 \mathrm{mph}$
C) $\frac{160}{9} \mathrm{mph}$
D) $\frac{9}{160} \mathrm{mph}$

Question

Quizplus · Accepted Answer

Since speed varies inversely with time, we can set up the relationship as $s_1t_1 = s_2t_2$, where $s_1 = 40$ mph, $t_1 = 45$ minutes (or $\frac{3}{4}$ hours), and $t_2 = 20$ minutes (or $\frac{1}{3}$ hours). Solving for $s_2$, we get $s_2 = \frac{s_1t_1}{t_2} = \frac{40 \times \frac{3}{4}}{\frac{1}{3}} = 90$ mph.

The Speed of a Vehicle Varies Inversely as the Time 452mph\frac{45}{2} \mathrm{mph}245​mph

The Speed of a Vehicle Varies Inversely as the Time $\frac{45}{2} \mathrm{mph}$