SOLUTION: The speed of a stream is 5mph. If a boat travels 66 miles down stream in the same time that it takes to travel 33 miles upstream. What is the speed of the boat in still water?

Click here to see ALL problems on Travel Word Problems

Question 182578: The speed of a stream is 5mph. If a boat travels 66 miles down stream in the same time that it takes to travel 33 miles upstream. What is the speed of the boat in still water?
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
The speed of a stream is 5mph. If a boat travels 66 miles down stream in the same time that it takes to travel 33 miles upstream. What is the speed of the boat in still water?
--------------------------
Call the speed of the boat b
Going downstream, the speed relative to the dirt is b+5
Upstream, it's b-5
t = time
t = 66/(b+5)
t = 33/(b-5)
--------------
66/(b+5) = 33/(b-5)
66(b-5) = 33(b+5)
66b-330 = 33b+165
33b = 495
b = 15 mph

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Relative to the bank of the river, the boat travels the speed in still water plus the speed of the current when going downstream, and speed in still water minus the speed of the current when going upstream.

The speed of the current is 5 mph, so if the speed of the boat in still water is r, the downstream speed is r + 5, and the upstream speed is r - 5.

Since distance equals rate times time, , we also know that time equals distance divided by rate, .

So the time for the downstream trip must be:

While the time for the upstream trip must be:

But these times are equal so:

Giving us a simple proportion. Cross-multiply:

Divide both sides by 33:

Distribute and collect:

Checking the answer is left as an exercise for the student.

John