Question

a motorboat travels 371 kilometers in 7 hours going upstream. it travels 525 kilometers going downstream in the same amount of time. what is the rate of the boat in still water and what is the rate of the current?

Answer 1

Speed of boat in still water = 64 km/hr

Speed of the current = 11 km/hr

Explanation:

Let the speed of motorboat in still water = x km/hr

Let the speed of current = y km/hr

Motorboat travels 371 km in 7 hours going upstream.

Speed of motorboat while going upstream = speed of motorboat in still water - speed of current = (x-y)

=>
`\[x-y = (371)/(7)\]`

=>
`\[x-y = 53\]` ------------------------------(1)

Motorboat travels 525 km in 7 hours going downstream.

Speed of motorboat while going downstream = speed of motorboat in still water + speed of current = (x+y)

=>
`\[x+y = (525)/(7)\]`

=>
`\[x+y = 75\]` -----------------------------(2)

Solving for x and y from (1) and (2):

Adding (1) and (2):

2x = 128

=> x = 64

Substituting the value of x in (1), y = 11