Question

Sarah left Minneapolis heading east on the interstate at a speed of 70 mph. Her sister followed her on the same route, leaving 2 hours later and driving at a rate of 80 mph. How long will it take for Sarah's sister to catch up to Sarah?

Answer 1

To determine the time it will take for Sarah's sister to catch Sarah, we calculate the head start distance Sarah gained and divide it by their relative speed. Sarah's sister will catch up in 14 hours.

Step-by-step explanation:

The subject of this question is Mathematics, specifically it involves solving problems related to relative speed and time in motion. To find out how long it will take for Sarah's sister to catch up to Sarah, we need to calculate the time it takes for the sister driving at 80 mph to cover the distance head start that Sarah, driving at 70 mph, has gained by leaving 2 hours earlier.

First, we determine the head start distance that Sarah achieved:

• Head start = Sarah's speed × lead time = 70 mph × 2 hours = 140 miles

Next, we calculate the relative speed between the two sisters:

• Relative speed = Sister's speed - Sarah's speed = 80 mph - 70 mph = 10 mph

Finally, we find out how long it will take the sister to catch up:

• Time to catch up = Head start ÷ Relative speed = 140 miles ÷ 10 mph = 14 hours

Therefore, it will take Sarah's sister 14 hours to catch up to Sarah from the time she began her own journey.