Question

a boat takes 4 hours to go 20 miles upstream.It can go 32 miles downstream in same time.Find the rate of the current and the rate of the boat in still water.

Answer 1

Upstream: It goes about 5 mph b/c 20 miles/4 hours= 5 mph Downstream:It goes about 8 mph b/c 32 miles/ 4 hours=8 mph Hope I helped! :-)

Answer 2

Let

x---------> the rate of the boat in still water in mph

y--------> the rate of the current in mph

we know that

Upstream

`rate=(20)/(4) \\\\ rate=5mph`

`x-y=5` equation
`1`

Downstream

`rate=(32)/(4) \\\\ rate=8mph`

`x+y=8` equation
`2`

Adds equation
`1` and equation
`2`

`x-y=5\\ x+y=8\\ -----\\ 2x=13\\ x=6.5mph`

Find the value of y

`x+y=8\\ y=8-x\\ y=8-6.5\\ y=1.5 mph`

therefore

the answer is

the rate of the boat in still water is
`6.5 mph`

the rate of the current is
`1.5 mph`