A motorboat can maintain a constant speed of 13 miles per hour relative to the water. The boat makes a trip upstream to a certai

Question

Mars2501 [29]

4 years ago

6

A motorboat can maintain a constant speed of 13 miles per hour relative to the water. The boat makes a trip upstream to a certai

n point in 63 minutes; the return trip takes 15 minutes. What is the speed of the current?

Mathematics

1 answer:

lara [203] · Answer 1 · 2021-12-30T14:53:23+03:00

Answer:

8 mph

Step-by-step explanation:

The speed in each direction is the speed of the boat with the speed of the current appropriately added. If x is the speed of the current, the upstream speed is 13-x; the downstream speed is 13+x.

The ratio of times is inversely proportional to the ratio of speeds, so we ahve ...

15/63 = 5/21 = (13-x)/(13+x)

5(13 +x) = 21(13 -x) . . . . . . . cross multiply

26x = 13(21 -5) = 13·16

x = 13·16/26 = 16/2 = 8

The speed of the current is 8 miles per hour.