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Puzzle Details

Kevin and Daniel 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?

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. QED.

There are a number of ways of working this out, and here are two of them:

Method 1
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:

D     D     3
-  -  -  =
2     4

Multiplying throughout by 2, and then 4, gives:

4D - 2D = 24

So:

2D = 24

And:

D = 12 miles.

They rowed 12 miles upstream. QED.

Method 2
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

Giving:

2H = 4H - 12

Rearranging gives:

12 = 2H

So:

H = 6 hours.

They rowed for 6 hours upstream at 2 miles per hour, which is a total of 12 miles. QED.

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