SOLUTION: A BOAT TRAVELS 52 MILES UP THE RIVER IN THE SAME AOUNT OF TIME IT TAKES TO TRAVEL 92 MILES DOWN THE SAME RIVER. IF THE CURRENT IS 5 MILES PER HOUR, WHAT IS THE SPEED OF THE BOAT IN

Question 115098: A BOAT TRAVELS 52 MILES UP THE RIVER IN THE SAME AOUNT OF TIME IT TAKES TO TRAVEL 92 MILES DOWN THE SAME RIVER. IF THE CURRENT IS 5 MILES PER HOUR, WHAT IS THE SPEED OF THE BOAT IN STILL WATER ?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
HEY! Ease up on the ALL CAPS.

Remember the formula for distance, rate, and time: .

We want to find the boat's speed through the water, so lets call that r.

The boat goes up river against the current, so the speed relative to the land is 5 miles per hour less than the speed through the water, or r - 5.

The boat goes down river with the current, so the speed is 5 mph more, or r + 5.

First let's rearrange the formula so that it is in terms of time:

The amount of time the boat traveled up river is then given by and the time down river is given by . And we know from the problem statement that these two times are equal, so:

, Cross-multiply the proportion

, Distribute

, Collect like terms

, Divide by 40

And the speed of the boat through the water is 18 miles per hour.

Last step, VERY important: Check your answer.

Since both times (4 hours) are equal, the answer checks.

Hope that helps,
John
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