SOLUTION: Can someone please walk me through these? a) It takes a groundskeeper 45 minutes to prepare a softball field for a game. It takes his assistant 50 minutes to prepare the same fi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Can someone please walk me through these? a) It takes a groundskeeper 45 minutes to prepare a softball field for a game. It takes his assistant 50 minutes to prepare the same fi      Log On


   

Question 232419: Can someone please walk me through these?
a) It takes a groundskeeper 45 minutes to prepare a softball field for a game. It takes his assistant 50 minutes to prepare the same field. How long will it take if they work together to prepare the field?
____ minutes
b) It takes the owner/operator of a dog kennel 7 hours to clean all of the cages. It takes his assistant 4 hour(s) more than that to clean the same cages. How long will it take if they work together?
____ hours
Thank you,
John
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a) It takes a groundskeeper 45 minutes to prepare a softball field for a game. It takes his assistant 50 minutes to prepare the same field. How long will it take if they work together to prepare the field?
G does 1/45 job per minute
A does 1/50 job per minute
Together, they do 1/45 + 1/50 = 19/450 jobs/minute
--> 450/19 minutes to do the job
You can use a shortcut, product/sum
50*45/(50+45) = 2250/95
= 450/19
--------------------------------
b) It takes the owner/operator of a dog kennel 7 hours to clean all of the cages. It takes his assistant 4 hour(s) more than that to clean the same cages. How long will it take if they work together?
This is 7 and 11 hours.
7*11/(7+11) = 77/18 hours
= ~ 4.28 hours

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a) It takes a groundskeeper 45 minutes to prepare a softball field for a game. It takes his assistant 50 minutes to prepare the same field. How long will it take if they work together to prepare the field?
____ minutes
=================================
grdnskeeper rate : (1/45) job per minute
assistant rate:::: (1/50) job per minute
together rate::::: (1/x) job per minute
--------------------
Equation:
rate + rate = together rate
1/45 + 1/50 = 1/x
(50+45)/(45*50) = 1/x
x = (45*50)/(45+50)
x = 23.68 minutes (time for them to do the job together
==============================================================

b) It takes the owner/operator of a dog kennel 7 hours to clean all of the cages. It takes his assistant 4 hour(s) more than that to clean the same cages. How long will it take if they work together?
---
Same procedure:
Equation:
(1/7) + (1/11) = 1/x
x = (7*11)/(7+11)
x = 4.28 hrs (time for them to do the job together)
===================
Cheers,
Stan H.