a motorboat takes 5 hours to travel 100 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

Vb = Vboat

Vs=vstream

For upstream case Vb-Vs is the net speed = 100/5 = 20 MPH

For downstream case Vb+vs is the net speed = 100/2 = 50 MPH

Vb = 35 MPH (speed of boat in still water)

Vs = 15 MPH ( speed of stream)

Answer 2

Let Vb = the speed of the boat, and Vw = the speed of the water. From the problem statement, we know that Vb > Vw

we have two unknowns, so we need 2 equations:

Upstream:

The combined speed is Vb - Vw. Write an equation for the distance, which is the product of time and speed:

100 = 5*(Vb - Vw) #1

Downstream:

Speed = Vb + Vw

100 = 2*(Vb + Vw) #2

Divide #1 by 5 and divide #2 by 2:

20 = Vb - Vw

50 = Vb + Vw

Add the equations to get:

70 = 2Vb

So Vb = 35, and--from any equation--Vw = 15