Alex and Blake were rowing their canoe along the River Trent.
In the morning they managed to row upstream at an average speed of 2 miles per hour.
They then stopped for a spot of lunch and a nice rest.
In the afternoon, the pace was a little easier as they were now rowing downstream back to their starting point, and managed an average speed of 4 miles an hour.
The morning trip took them 3 hours longer than the afternoon.
How far did they row upstream?
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You can either fix the distance rowed and see what numbers work, or you can fix the number of hours.
In the morning, rowing at 2 miles per hour, they rowed for 6 hours. In the afternoon, rowing at 4 miles per hour, they rowed for 3 hours.
There are a number of ways of working this out, and here are two of them:
If we assume the distance the rowed upstream to be D miles, we know the morning took (D ÷ 2) hours, and the afternoon took (D ÷ 4) hours, with a difference of 3 hours. So:
- - - = 3
Multiplying throughout by 4 gives:
2D - D = 12
D = 12 miles
They rowed 12 miles upstream.
If we assume they rowed for H hours upstream, we know they travelled H x 2 miles in the morning. In the afternoon they rowed for (H - 3) hours, and travelled (H - 3) x 4 miles. We know these distances are the same, so:
2H = (H - 3) x 4
2H = 4H - 12
12 = 2H
H = 6 hours
They rowed for 6 hours upstream at 2 miles per hour, which is a total of 12 miles.
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