Arower travels upstream at 6km per hour and back to the starting point at 10km per hour. total journey takes 48 minutes. how far upstream did the rower go?

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

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

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.

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.

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step-by-step explanation: