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Puzzle 505
Exactly how many minutes is it before seven o'clock, if 40 minutes ago it was three times as many minutes past two o'clock?
Hint
How many minutes are there between 2:00 and 7:00?
Answer
65 minutes.
Reasoning
We need to break down the five hours in the following way:
3 x Answer minutes past two o'clock40 minutesAnswer minutes before seven o'clock
Why? It is now Answer minutes before seven o'clock, and then we have the 40 minutes before that, and the remaining time was 3 x Answer minutes past two o'clock.
So, five hours = 5 x 60 = 300 minutes. We already know about the 40 minutes, so we have to share the remaining 260 minutes in the ratio 3:1, which gives 195:65 minutes. Or using algebra 4 x Answer = 300 – 40, so Answer = 65 minutes.
Therefore, the five hours is made up of:
195 minutes past two o'clock40 minutes65 minutes before seven o'clock
So, it's currently 65 minutes before 7:00 = 5:55.
Double-Checking
It is now 65 minutes before seven o'clock = 5:55, so 40 minutes ago it was 5:15 – which is 195 minutes after 2:00, as required (as 65 x 3 = 195).
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Puzzle 506
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.
There are usually around 206 bones in an adult human body, and 365 or 366 days in a year.
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It is now three years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
