Question

At 1:30 p.m., Tom leaves in his boat from a dock and heads south. He travels at a rate of 25 miles per hour. Ten minutes later, Mary leaves the same dock in her speedboat and heads after Tom. If she travels at a rate of 30 miles per hour, when will she catch up with Tom

Answer 1

Answer: she would catch up with Tom in 1 hour.

Step-by-step explanation:

Let t represent the time it will take for Mary to catch up with Tom.

Tom leaves his boat from a dock and travels at a rate of 25 miles per hour.

Distance = speed × time

Distance travelled by Tom in t hours is

25 × t = 25t

Ten minutes later, Mary leaves the same dock in her speedboat and heads after Tom. Converting 10 minutes to hours, it becomes 10/60 hour

Time spent by Mary is (t - 10/60) hours. If she travels at a rate of 30 miles per hour, it means that the distance that she would travel in

(t - 10/60) hours is

30(t - 10/60)

= 30t - 5

By the time she catches up with Tom, they would have covered the same distance. It means that

25t = 30t - 5

30t - 25t = 5

5t = 5

t = 5/5 = 1 hour