Question

Boat A and Boat B are racing across a bay. Boat A is 6 miles ahead of Boat B. Boat A has a top speed of 36 miles per hour, but Boat B has a top speed of 44 miles per hour.

Part A:


If both boats are traveling at their top speeds, how long will it take Boat B to catch up with Boat A?






Part B:


How far will Boat B have traveled when it has caught up to Boat A?

Answer 1

45 min = 0.75 hours

Explanation:

Since Boat A is 6 miles ahead of boat B and has a top speed of 36 miles per hour, the distance it moves in time, t is d = 6 + 36t where 36t is the distance it moves in time, t with speed 36 miles per hour.(36t = 36 miles per hour × t hours)

Also, since Boat B has a top speed of 44 miles per hour, the distance d' it moves in time, t with this speed is

d'= 44t (44t = 44 miles per hour × t hours)

When Boat B catches up with Boat A, their distances are equal. So,

d = d'

6 + 36t = 44t

subtracting 36t from both sides, we have

44t - 36t = 6

simplifying

8t = 6

dividing through by 8, we have

t = 6/8 hours

t = 0.75 hours

t = 0.75 × 60 min

t = 45 min