Commuting from work to home, a lab technician traveled 10 mi at a constant rate through congested traffic. On reaching the expressway, the technician's speed increased by 22 mph. An additional 20 mi was traveled at the increased speed. The total time for the trip was 1 h. Find the rate of travel through the congested traffic.
A) 19.4 mph
B) 27.4 mph
C) 20.4 mph
D) 18.4 mph
E) 28.4 mph

Question

Quizplus · Accepted Answer

Let the rate of travel through congested traffic be $x$ mph. The time to travel the first 10 miles is $\frac{10}{x}$ hours. The speed on the expressway increases to $x + 22$ mph, so the time to travel the next 20 miles is $\frac{20}{x + 22}$ hours. The total time for the trip is 1 hour, so we have the equation: $\frac{10}{x} + \frac{20}{x + 22} = 1$. Solving this equation for $x$ gives $x = 19.4$ mph.

Commuting from Work to Home, a Lab Technician Traveled 10