Hint: You can either fix the distance rowed and see what numbers work, or you can fix the number of hours.
Answer: 12 miles.
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:
D D 3
- - - =
Multiplying throughout by 2, and then 4, gives:
4D - 2D = 24
2D = 24
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.
Starting in the bottom left corner and moving either up or right, adding up the numbers along the way, what is the largest sum which can be made?