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?
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?
From brainbashers.com