Question

The Hopewells are moving across the country. Mr. Hopewell leaves 4 hours before Mrs. Hopewell. If he averages 35 mph and she averages 85 mph, how many hours will it take Mrs. Hopewell to catch up to Mr. Hopewell?

A) 7
B) 8
C) 9
D) 10

Answer 1

To calculate the time for Mrs. Hopewell to catch up to Mr. Hopewell, we find the distance he traveled and divide it by their relative speed. The calculation shows it will take Mrs. Hopewell 2.8 hours to catch up, which is not one of the provided multiple-choice answers.

Step-by-step explanation:

The question asks how long it will take Mrs. Hopewell to catch up to Mr. Hopewell given their average speeds and the head start time of Mr. Hopewell. To solve this, we can use the concept of relative speed and the formula for distance, which is distance = speed × time.

Step-by-step solution:

1. Calculate the distance Mr. Hopewell travels in 4 hours at 35 mph: distance = 35 mph × 4 hours = 140 miles.
2. Find the relative speed at which Mrs. Hopewell is gaining on Mr. Hopewell: relative speed = 85 mph - 35 mph = 50 mph.
3. Calculate the time it takes Mrs. Hopewell to catch up: time = distance / relative speed = 140 miles / 50 mph = 2.8 hours.

Therefore, it will take Mrs. Hopewell 2.8 hours to catch up to Mr. Hopewell, which is not one of the options provided in the multiple-choice question. Since 2.8 hours is not exactly 3 hours, it appears there may have been a mistake or typo in the multiple-choice answers given.