Question 99497: Help! PLEASE! I can't seem to figure these out!
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?
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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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