Question

Rick set out on his bike for a cookout at church, traveling at 10 mi/hr. Fifteen minutes later, his mother, realizing that he had forgotten the hot dogs he signed up to bring, set out in the car to catch him. If she drove 40 mi/hr, how long did it take her to catch up with him?

A) 5 minutes
B) 7.2 minutes
C) 10 minutes
D) 20 minutes
E) 30 minutes
F) None of the above.

Answer 1

Rick's mother took 5 minutes to catch up with him.

Step-by-step explanation:

To determine how long it took Rick's mother to catch up with him, we need to find the time it took for her to travel the same distance as Rick but at a faster speed.

Since Rick travels at 10 mi/hr and his mother drives at 40 mi/hr, their relative speed is 40 - 10 = 30 mi/hr.

Converting the time to hours, 15 minutes is equivalent to 15/60 = 0.25 hours.

We can set up the equation: distance = speed x time. Rick's distance is 10 x (0.25 + t) miles, where t is the extra time it takes for his mother to catch up.

His mother's distance is 40 x t miles since she starts later but catches up to Rick.

Setting both distances equal to each other, we have 10 x (0.25 + t) = 40 x t.

Simplifying the equation gives us 2.5 + 10t = 40t.

Subtracting 10t from both sides gives us 2.5 = 30t.

Dividing both sides by 30 gives us t = 2.5/30 = 1/12 hours, which is equivalent to 5 minutes.

Therefore, it took Rick's mother 5 minutes to catch up with him.