Question 240752
If Bob can mow a lawn in 3 hours and Joe can do it in 5 hours, how long would it take them together? 
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Let t = time required when they work together (assuming two lawn mowers)
let the completed job = 1
:
{{{t/3}}} + {{{t/5}}} = 1
clear the denominators, multiply by 15:
15*{{{t/3}}} + 15*{{{t/5}}} = 15(1)
cancel the denominators:
5t + 3t = 15
8t = 15
t = {{{15/8}}}
t = 1.875 hrs or 1 + .875(60) = 1 hr 52.5 min
;
:
Check solution in the original shared work equation:

1.875/3 + 1.875/5 = 
.625 + .375 = 1
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:
The larger hose can fill the pool by itself in 10 hours, 
The smaller hose can fill the pool in 15 hours. 
Unfortunately, I left the drain open in the pool and it can drain the pool in 20 hours. 
How long will it take before the pool is filled with both hoses running and the drain open
:
Let t = time required to fill the pool with this situation
Let the full pool = 1
Use + for filling and - for draining
:
{{{t/10}}} + {{{t/15}}} - {{{t/20}}} = 1
Clear the denominator by multiplying by 60
:
Use the 1st one as an example, you should be able to do this by yourself.