A boat traveled 72 miles downstream and back. The trip downstream took 3 hours. The trip back took 9 hours. What is the speed of the boat in still water?

Question

A boat traveled 72 miles downstream and back. The trip downstream took 3 hours. The trip back took 9 hours. What is the speed of the boat in still water? What is the speed of the current?

Answer 1

Distance = Rate * time

72 mi = R * 3 hr

24 ^mi/^hr = R downstream

 

72 mi = R * 9 hr

8 ^mi/^hr = R upstream

 

let v be the velocity of the boat and c = the velocity of the river:

v + c = 24 ^mi/^hr

v - c = 8 ^mi/^hr

 

Isolating v, we get:

v = 24 ^mi/^hr - c

v = 8 ^mi/^hr + c

Which then means:

24 ^mi/^hr - c = 8 ^mi/^hr + c

 

24 ^mi/_hr = 8 ^mi/^hr + 2c

16 ^mi/_hr = 2c

8 ^mi/_hr = c

So the river current is 8 ^mi/_hr

 

v = 8 ^mi/_hr + 8 ^mi/_hr

v = 16 ^mi/_hr

v = 24 ^mi/_hr - 8 mi/_hr

v = 16 ^mi/_hr

 

So the velocity of the boat in still water is 16 ^mi/_hr