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

Let

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

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

we know that

Upstream

$rate=\frac{20}{4} \\\\ rate=5mph$

$x-y=5$ equation $1$

Downstream

$rate=\frac{32}{4} \\\\ rate=8mph$

$x+y=8$ 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 $1.5 mph$

Answer 2

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! :-)