Question 503644
The cold-water faucet fills a bathtub in 12min, and the hot-water faucet fills the bathtub in 10min.
 If you remove the stopper, a full tub will empty in 6min. How long will it take to fill the tub if both faucets are on and the stopper is removed?
:
Let t = time to fill the tub with both faucets and drain open
Let a full tub = 1
:
{{{t/12}}} + {{{t/10}}} - {{{t/6}}} = 1
multiply by 60, to clear the denominators
60*{{{t/12}}} + 60*{{{t/10}}} - 60*{{{t/6}}} = 1
cancel the denominators and you have:
5t + 6t - 10t = 60
11t - 10t = 60
t = 60 minutes