A boat travels 210 miles downstream in 10 hours. The return trip upstream takes 70 hours. Find the speed of the current and the speed of the boat in still water?

Question

A boat travels 210 miles downstream in 10 hours. The return trip upstream takes 70 hours. Find the

Answer 1

Sorry about those awful drawings, I'm an Algebra 2 tutor, not a boat designer 😬

Answer 2

210 = 10(b + c)

210 = 70(b - c)

21 = b + c

21 = 7b - 7c

147 = 7b + 7c

21 = 7b - 7c

168 = 14b

12 = b

Can you determine the speed of the current?

Answer 3

Let x= speed of boat in still water

y=speed of current

x+y= speed downstream (boat is working with the current, so the speed of the boat

increases by the value of the current’s speed)

x-y= speed upstream (boat is working against the current, so the boat’s speed

decreases by the value of the speed of the current)

To find speed downstream, divide miles by hours to get speed in mph.

210/10=21 mph (speed downstream)

x+y=21 (1)

To find speed upstream, divide miles by hours to get speed in mph.

210/70=3 mph (speed upstream)

x-y=3 (2)

Equations (1) and (2) form the following system of equations, which is to be solved for x (speed of boat in still water), and y (speed of current):

x+y=21

x-y=3

to solve system of equations, add both equations together:

(x+y)+(x-y)=21+3

2x=24

x=12 —> so speed of boat in still water is 12 mph

plug x=12 back into one of the equations, and solve for y

x+y=21 —> 12+y=21 —> y=9 —> so speed of current is 9 mph