SOLUTION: i do not understand how to even start this problem. it says: With your new lawn mower, you can mow a lawn in 4 hours. With an older mower, your friend can mow the same lawn in 5

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Question 54537This question is from textbook McDougal Littell Algebra 1 concepts and skills
: i do not understand how to even start this problem. it says:
With your new lawn mower, you can mow a lawn in 4 hours. With an older mower, your friend can mow the same lawn in 5 hours. How long will it take you to mow the lawn, working together?
HELP!This question is from textbook McDougal Littell Algebra 1 concepts and skills

Found 3 solutions by Nate, stanbon, Earlsdon:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Rate: 1/4
Time = t
Rate * Time = Work
t/4 = Work
Rate: 1/5
Time = t
Work = t/5
t/4 + t/5 = 1
20t/4 + 20t/5 = 20
5t + 4t + 20
9t = 20
t = 20/9
or 2 hours 13 minutes

Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
With your new lawn mower, you can mow a lawn in 4 hours. With an older mower, your friend can mow the same lawn in 5 hours. How long will it take you to mow the lawn, working together?
-----------
New Mower DATA:
Time to mow lawn = 4 hr/job ; rate= (1/4)job/hr.
------------
Old Mower DATA:
Time to mow lawn = 5 hr/job ;rate= (1/5) job/hr.
--------------
Working together DATA:
Time to mow lawn ; x hr/job ; rate = (1/x) job/hr.
----------
EQUATION:
new rate + old rate = together rate
1/4 +1/5 = 1/x
(9/20)=1/x
x=20/9
x=2 2/9 hrs. or 2 hr 13 1/3 minutes (This is the time to mow the
lawn when both mowers are used.)
Cheers,
Stan H.

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Find the rate at which each of you can mow the lawn:
If you can mow the lawn in 4 hours, then you can mow 1/4 of the lawn in 1 hour.
If your friend can mow the same lawn in 5 hours, then he/she can mow 1/5 of the lawn in 1 hour.
So together, the two of you can mow 1/4 + 1/5 of the lawn in 1 hour.
1/4 + 1/5 = (5+4)/20 = 9/20 of the lawn in 1 hour.
So, it will take you both 20/9 hours to mow the lawn together.
20/9 hours = 2 hrs and 13 1/3 minutes.