Question 99497
1. One number is 6 more than another number. The sum of the sumbers is one more than 3 times their difference. What are the numbers?
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Let one of the numbers be "x"; the other number is "x+6"
EQUATION:
x + x+6 = 3(x+6-x) + 1
2x+6 = 18+1
x = 13/2
x = 6.5 (one of the numbers)
x+6 = 12.5 (the other number)
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2. In a small rowboat, it took Alice 6 hours to go 6 miles upstream, but she was able to return to her starting point in only 45 minutes. Assuming her rowing speed was constant, what was the speed of the current?
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Upstream DATA:
distance=6 miles ; time = 6 hrs; rate = d/t= 1 mph
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Downstream DATA:
distance = 6 miles ; time = (3/4) hr ; rate = d/t = 6/(3/4) = 8 mph
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Let speed in quiet water be "b"; let speed of stream be "s"
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EQUATIONS:
b+s = 8 mph
b-s = 1 mph
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Add to get:
2b = 9mph
b = 4.5 mph (speed of boat in quiet water)
Substitue to solve for "s":
4.5+s = 8
s = 3.5 mph (speed of the stream)
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Cheers,
Stan H.