Question

A motor boat travels 48 miles down a river in two hours but takes twice as long to make the return trip upstreamFind the speed of the boat in still water and the rate of the current

Answer 1

speed of the current is 6 miles per hour.

Speed of the boat in still water is 18 miles per hour

Explanation:

-Speed is defined as displacement over time.

-Let a be the speed in still water and b be speed of the current of the river.

#The speed downstream is equated as:

`2(a+b)=48`

#The speed upstream in 4hrs is equated as:

`4(a-b)=48`

we make a the subject of the formula in i and substitute in ii:

`2a+2b=48\\\\a+b=24\\\\a=24-b\\\\\\\#substitute \ in \ ii\\\\4a-4b=48\ \ \ =>a-b=12\\\\\therefore (24-b)-b=12\\\\b=6\\\\a=24-b=24-6\\\\a=18`

Hence, speed of the current is 6 miles per hour and

Speed of the boat in still water is 18 miles per hour