Question

If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________?

Answer 1

rate of the river 7 mi/hr

rate of the boat 17 mi/hr

Step-by-step explanation:

Let the speed of the boat be x and the speed of the river be y.

When the boat is going down stream, we add the speed of both since they are moving in the same direction

x + y = 72 mi/3 hr ⇒ x + y = 24 ...(1)

When the boat is going down stream, we subtract the velocity of the river since it slows the boat down

x - y = 60 mi/6 hr which can be rewritten as x = y + 10 ....(2)

Now we solve simultaneously by substituting equation (2) into (1)

x + y = 24

(y + 10) + y = 24

2y = 14

y = 7

x = 17