A boat travels 30 miles upstream in 4 hours. The trip downstream takes 2.5 hours. Find the rate of he boat in still water.

Guest Mar 5, 2017

#1**0 **

30 / 4 = 7.5 mph - the boat's speed upstream

30 2.5 = 12 mph - the boat's speed downstream

12 - 7.5 = 4.5 mph - the speed of the current both ways

4.5 / 2 = 2.25 mph - The actual speed of the current.

7.5 + 2.25 =9.75 mph - the speed of the boat in still water, which is the same as:

12 - 2.25 =9.75 mph

Guest Mar 5, 2017

#2**+5 **

We have that D/T = R

Let the speed in still water be S and let the current speed = C

So....the rate with the current is S + C and the rate going against the current is S - C

And we know that

30/ 2.5 = S + C

12 = S + C (1) and

30/4 = (S - C)

7.5 + C = S (2)

Put (2) into (1)

12 = 7.5 + C + C

12 = 7.5 + 2C

4.5 = 2C divide both sides by 2

2.25 mph = C = rate of the current

And, using (2), the speed of the boat in still water = 7.5 + 2.25 = 9.75mph

CPhill
Mar 5, 2017