A boat travels 45 miles up the river in the same amount of time it takes to travel 85 miles down the same river. If the current is 4 miles per hour, what is the speed of the boat in still water? d r t Upstream Downstream
A) 4 miles per hour
B) 6.5 miles per hour
C) 10 miles per hour
D) 13 miles per hour
E) 7 miles per hour

Question

Quizplus · Accepted Answer

Let's say the speed of the boat in still water is x miles per hour. Then, the speed of the boat upstream (against the current) is (x-4) miles per hour, and the speed of the boat downstream (with the current) is (x+4) miles per hour. We can set up two equations using the formula distance = rate x time:

45 = (x-4) t

85 = (x+4) t

Since the time is the same in both cases, we can set the two equations equal to each other:

45/(x-4) = 85/(x+4)

Cross-multiplying and simplifying, we get:

85(x-4) = 45(x+4)

85x - 340 = 45x + 180

40x = 520

x = 13

Therefore, the speed of the boat in still water is 13 miles per hour.

A Boat Travels 45 Miles Up the River in the Same