A motorboat can go 16 miles downstream on a river in 20 minu

A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles.

a. Write an equation for the motion of the motorboat downstream.
b. Write an equation for the motion of the motorboat upstream.
c. Find the speed of the current.

Solution

Let the speed of the boat in still water = x
And the speed of the stream = y
When the boat goes downstream, the resultant speed = x+y
Given,A motorboat can go 16 miles downstream on a river in 20 minutes.
1) So we have, distance = speed*time
16 = (x+y)*(20/60)
16 = (x+y)*(1/3)
48 = x+y
x+y=48 ...(1)
2) When the boat goes upstream, the resultant speed = x-y
It takes 30 minutes for this boat to go back upstream the same 16 miles.
So we have, distance = speed*time
16 = (x-y)*(30/60)
16 = (x-y)*(1/2)
32 = x-y
x-y=32 ...(2)
3) Solving (1) and (2),
(1)+(2)=> 2x = 48+32
2x = 80
x = 80/2
x = 40
Substituting in (1), we get
40+y = 48
y = 48-40
y = 8