Question 1115037: Jessie paddled her canoe 20 miles upstream, then paddled back. If the speed of the current was
3 mph and the total trip took 7 hours, what was Jessie’s speed?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
If x is her speed in still water, then her speed upstream is x-3, and her speed downstream is x+3.
The time for the upstream trip is 20/(x+3); the time for the downstream trip is 20/(x-3).
Since the total time is 7 hours...
Multiply both sides of the equation by the common denominator, (x+3)(x-3); you will get a quadratic equation which has one positive root and one negative. Obviously the positive root is the answer to the question.
I leave the details of the algebra to you.
Here is a way to solve the problem without the algebra by using logical reasoning.
Note that the total time for the trip upstream and back is 7 hours. Not 7.2 hours; not 7 hours, 3 minutes, and 43 seconds. EXACTLY 7 hours.
Because the total trip time is a whole number of hours, the times for each leg of the trip are almost certain to be whole numbers.
Now look at the basic equation for solving the problem. 20 divided by x+3 should be a whole number; and 20 divided by x-3 should be a whole number.
So you need to find two numbers whose difference is 6 (the difference between x+3 and x-3) that are both divisors of 20.
The divisors of 20 are 1, 2, 4, 5, 10, and 20. The only two that have a difference of 6 are 4 and 10.
So her upstream speed is 4mph and her downstream speed is 10mph; 20/4 + 20/10 = 5+2 = 7 hours.
And since the speed of the current is 3mph, her speed in still water is 7mph.
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