Solve the problem.
-Tom Quig traveled 220 miles east of St. Louis. For most of the trip he averaged $60 \mathrm{mph}$, but for one period of time he was slowed to $20 \mathrm{mph}$ due to a major accident. If the total time of travel was 7 hours, how many miles did he drive at the reduced speed?
A) 95 miles
B) 110 miles
C) 100 miles
D) 120 miles

Question

Quizplus · Accepted Answer

Let the time spent at 20 mph be $t$ hours. Then, the time spent at 60 mph is $7-t$ hours. The distance covered at 20 mph is $20t$ miles, and the distance covered at 60 mph is $60(7-t)$ miles. The total distance is 220 miles, so we have the equation $20t + 60(7-t) = 220$. Solving for $t$ gives $t = 3$ hours. Therefore, the distance driven at the reduced speed is $20 \times 3 = 60$ miles. However, there seems to be a mistake in my initial explanation. Let's correct the approach:Let $x$ be the distance traveled at 20 mph, and $220-x$ be the distance traveled at 60 mph. The time spent at 20 mph is $\frac{x}{20}$ hours, and the time spent at 60 mph is $\frac{220-x}{60}$ hours. The total time is 7 hours, so we have the equation $\frac{x}{20} + \frac{220-x}{60} = 7$. Solving this equation correctly will give us the right distance traveled at 20 mph. Upon correctly solving the equation, we find that the distance traveled at 20 mph is indeed 100 miles, which matches option C. My initial explanation contained a calculation error, and upon reevaluation, the correct distance driven at the reduced speed is 100 miles, not 60 miles as previously stated.

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