If one small rabbit can dig a warren in nine hours, a medium rabbit can dig a warren in 6 hours, and a large rabbit can dig a warren in four and a half hours.
How long will it take one small, one medium, and one large rabbit, to dig a warren if they all work together?
Answer
The two sons rowed to safety first, one son rowed back.
I rowed to safety and the other son rowed back to the island.
The two sons rowed to safety first, one son rowed back again.
My wife rowed to safety and the other son rowed back.
Finally, the two sons rowed to safety.
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Puzzle 3
A trout's tail weighs eight pounds.
Its head weighs as much as the tail and one-half of the body combined, and the body weighs as much as the head and tail combined.
The head weighs 24 pounds, the body weighs 32 pounds, and the tail weighs 8 pounds.
Reasoning
The trout is made up of the head, body and tail, H, B and T.
We are told that:
T = 8
(1) H = T + B ÷ 2
(2) B = H + T
Placing T into (1) and (2) we get:
(3) H = 8 + B ÷ 2
(4) B = H + 8
Using (4) in (3) we get:
H = 8 + B ÷ 2
(5) H = 8 + (H + 8) ÷ 2
Multiplying (5) by 2 we get:
2H = 16 + H + 8
2H = 24 + H
H = 24
Therefore, by (2):
B = H + T
B = 24 + 8
B = 32
Giving:
H = 24 B = 32 T = 8
And a total of 24 + 32 + 8 = 64 pounds.
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Puzzle 4
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.
