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Question 1143289: On a particular day, the wind added 5 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 5 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 42 miles with the wind, she could go only 22 miles against the wind.
What is her normal rowing speed with no wind?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
rate = x for jaime without the wind.
t = time.
d = distance.
with the wind, the formula for jaime becomes (x + 5) * t = 42
against the wind, the formula for jaime becomes (x - 5) * t = 22
simlify both equations to get:
xt + 5t = 42
xt - 5t = 22
subtract second equation from the first to get:
10t = 20
solve for t to get:
t = 2
in the first equation, replace t with 2 to get (x + 5) * 2 = 42
in the second equation, replace t with 2 to get (x - 5) * 2 = 22
simplify both equationt to get:
2x + 10 = 42
2x - 10 = 22
solve for x in both equations to get:
x = 16
first original equation becomes (16 + 5) * 2 = 42
second original equation becomes (16 - 5) * 2 = 22
evaluate both equations to get:
42 = 42
22 = 22
this confirms both equations are correct when t = 2 and when x = 16.
your solution is that jaime rows at 16 miles per hour without any wind.
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