SOLUTION: A coast guard cutter can sail 200 miles against the current in the same amount of time it can sail 260 miles with the current. If the current is 3 miles per hour, how fast can the

Question 1162960: A coast guard cutter can sail 200 miles against the current in the same amount of time it can sail 260 miles with the current. If the current is 3 miles per hour, how fast can the cutter sail in still water?
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

, so

Let represent the speed without the current. Then the upstream speed is and the downstream speed is .

For the upstream trip, the distance is 200, the rate is , and the time is , so:

For the downstream trip, the distance is 260, the rate is , and the time is , so:

Since we can say:

Solve for

John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The other tutor demonstrates one good algebraic method for solving the problem: setting the two time (=distance/rate) expressions equal to each other and solving the equation.

If you are good with mental arithmetic, the problem can be solved without algebra by setting up the problem differently.

Since the times are the same, the ratio of distances is equal to the ratio of the speeds:

The difference between numerator and denominator on the right is 6 -- so write the fraction on the left as an equivalent fraction in which the difference between numerator and denominator is also 6:

r+3 = 26 and r-3 = 20...

ANSWER: r = 23

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