Answers to last issue's Brain Teasers

1. My bath has two taps and a plug hole. The cold tap on its own fills the bath in 12 minutes, the hot one in 8 minutes. The plug hole can drain the bath in 24 minutes with the taps off. How long will the bath take to fill if I leave both taps on with the plug left out?
Answer: The key to the answer is to try and see how many baths can be filled in some number of hours that can be divided by 8, 12, and 24. Let us try 2 hours or 120 minutes.
In 2 hours, the cold tap could fill 120/12=10 baths, the hot tap could fill 120/8=15 baths and the plug could drain 120/24=5 baths.
So in 2 hours or 120 minutes, we have 10 + 15 - 5 baths full = 20 baths.  Therefore each bath would take 120/20 = 6 minutes to fill.

2. Practical Peter was asked to cut a 99 foot rope into three smaller, equal length ropes.
However, as usual, Pete couldn't find his measuring tape so he guessed! When he finally did find his tape (it was under his hat), he discovered that:
A) the second piece of rope was twice as long as the first piece, minus
35 feet (i.e. 2 x first, - 35).
B) the third piece of rope was half the length of the first, plus 15
feet (i.e. 0.5 x first, + 15)
How long were each of the pieces of rope?

Answer: This question can be solved easily using algebra, if we call the length
of the first rope A, we have:
    Rope 1 = A
    Rope 2 = 2 x A - 35
    Rope 3 = 0.5 x A + 15
The three ropes add to 99 feet, so:
    99 = Rope 1 + Rope 2 + Rope 3,
    99 = A + (2 x A - 35) + 0.5 x A + 15,
    99 = 3.5 x A - 20
Adding 20 to both sides we have: 119 = 3.5 x A, so A = 119 / 3.5 = 34 feet.
So the answer is, Rope 1 is 34 feet long, Rope 2 is 2 x 34 - 35 = 68 - 35 = 33 feet long, and Rope 3 = 0.5 x A + 15 = 0.5 x 34 + 15 = 17 + 15 = 32 feet long.
Just to check: Rope 1 + Rope 2 + Rope 3 = 34 + 33 + 32 = 99 feet.
From brainbashers.com