SOLUTION: The cross-country team left school and trotted to the duck pond at 3 mph. Then they ran back to the school at 7 mph. If the total trip took 10 hours, how far was it to the duck pon

Question 1202478: The cross-country team left school and trotted to the duck pond at 3 mph. Then they ran back to the school at 7 mph. If the total trip took 10 hours, how far was it to the duck pond?
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52898)   (Show Source): You can put this solution on YOUR website!
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Write the time equation + = 10 hours. Here d is one way distance, and the terms in the left side represent time to the pond and back, respectively. To solve equation, multiply both sides by 3*7. You will get 7d + 3d = 10*3*7 10d = 10*3*7 d = 3*7 = 21. ANSWER. The one-way distance is 21 miles. CHECK. Time to get pond is = 7 hours. Time to return back is = 3 hours. Total time is 7 + 3 = 10 hours. ! correct !

Solved.

Answer by greenestamps(13211)   (Show Source): You can put this solution on YOUR website!

The distances to the duck pond and back are the same, so the ratio of times at the two speeds is the opposite of the ratio of speeds.

The ratio of the two speeds was 3:7, so the ratio of times was 7:3. Since the total time was 10 hours, simple reasoning says they spent 7 hours going and 3 hours returning.

7 hours at 3 mph means the distance was 21 miles; likewise, 3 hours at 7 mph means the distance was 21 miles.

ANSWER: 21 miles

Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Going to, speed
Returning, speed
Total Trip time,
distance either direction, d
-

SPEEDS TIME DISTANCE GOING d RETURN d Total

multiply both sides by ;

To evaluate with your given values

.
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