Question

A boat takes 4 hours to go 8 miles upstream. It can go 32 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water.​ (Hint: Because the current pushes the boat when it is going​ downstream, the rate of the boat downstream is the sum of the rate of the boat and the rate of the current. The current slows down the boat when it is going​ upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the​ current.)

Answer 1

the rate of the boat = x mph

the rate of the​ current = y mph

the rate of the boat downstream =x+y

the rate of the boat upstream =x -y

Since,  boat takes 4 hours to go 8 miles upstream, using distance formula, velocity= distance/time

x-y= 8/4

x-y =2

Now, since boat takes 32 miles downstream in 4 hours,

x+y =32/4

x+y =8

Thus, sytem of equation is

x+y=8

x-y =2

Add both

2x =10

x=10/2

x=5

hence

y=8-5=3

Therefore,

the rate of the boat = 5 mph

the rate of the​ current =3 mph