Answer: The rower traveled 3 km upstream
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Explanation:
x = time it takes to go upstream
y = time it takes to go downstream
both time values are in hours
The rower goes some distance d for both the upstream and downstream journeys.
48 minutes = (48/60) hr = 4/5 hour
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Going upstream
distance = rate*time
d = r*t
d = 6*x
x = d/6 is the time it takes to go upstream
Going downstream
distance = rate*time
d = r*t
d = 10*y
y = d/10 is the time it takes to go downstream
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It takes d/6 hours to go upstream and d/10 hours to go downstream.
In total, it takes
d/6+d/10 = 5d/30+3d/30 = 8d/30 = 4d/15
hours to complete the round trip
Set this equal to 4/5 to get
4d/15 = 4/5
4d*5 = 15*4
20d = 60
d = 60/20
d = 3
This is the final answer.
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Optionally you can keep going to find the values of x and y
x = d/6
x = 3/6
x = 1/2 hour, or 30 minutes, is spent going upstream
y = d/10
y = 3/10 of an hour, or 18 minutes, is spent going downstream
in total, 30+18 = 48 minutes is spent on the round trip.
