A similar change is care, cares, caress, but these are not nouns.
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Puzzle 58
At the local racetrack, Alex was testing the latest car.
During the eight test laps, Alex managed to average the first two laps at 100mph, the next two laps at 102mph, the next two laps at 140mph, and the last two laps at 150mph.
The 8 laps were 40 miles, and using Speed = Distance ÷ Time: average speed = 40 ÷ (40/119) average speed = 40 x (119/40) = 119 mph
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Puzzle 59
Alex and Billie 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.
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:
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 4 gives:
2D − D = 12
So:
D = 12 miles
They rowed 12 miles upstream.
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.
