I found this math problem at Kitchen Table Math.
"769. An old brainteaser by Leonty Magnitsky: If a man drinks a barrel of water by himself in 14 days and the same barrel with his wife in 10 days, how many days would it take his wife to drink the barrel by herself?"
First of all, I find this easier to solve when the wording is changed to a barrel of vodka.
Here is my solution:
The sum of the fractional parts (man and wife) of drinking in one day is equal to the fractional part of both drinking in one day:
Let x = days wife takes to consume the whole barrel
1/14 + 1/x = 1/10
Multiply each side by the LCD to clear fractions:
10x + 140 = 14x
4x = 140
x = 35