SOLUTION: One good use for rational equations is the shared work problem. This solution would be of great help in scheduling employees. For example, If Bob can mow a lawn in 3 hours and Jo

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One good use for rational equations is the shared work problem. This solution would be of great help in scheduling employees. For example, If Bob can mow a lawn in 3 hours and Jo      Log On


   

Question 240752: One good use for rational equations is the shared work problem. This solution would be of great help in scheduling employees. For example, If Bob can mow a lawn in 3 hours and Joe can do it in 5 hours, how long would it take them together? Some people would be tempted to just average the two values and get the answer of four hours, but that would be wrong since Bob can do it by himself in 3 hours.
Solve this word problem using rational equations.
What is the relation of the shared work problem to the following problem?:
I am filling my pool with two hoses. 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?
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If Bob can mow a lawn in 3 hours and Joe can do it in 5 hours, how long would it take them together?
:
Let t = time required when they work together (assuming two lawn mowers)
let the completed job = 1
:
t%2F3 + t%2F5 = 1
clear the denominators, multiply by 15:
15*t%2F3 + 15*t%2F5 = 15(1)
cancel the denominators:
5t + 3t = 15
8t = 15
t = 15%2F8
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
:
:
:
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%2F10 + t%2F15 - t%2F20 = 1
Clear the denominator by multiplying by 60
:
Use the 1st one as an example, you should be able to do this by yourself.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
For example, If Bob can mow a lawn in 3 hours and Joe can do it in 5 hours, how long would it take them together?
----------------
Use the shortcut, product/sum
3*5/(3+5) = 15/8