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Jack usually mows his lawn in 3 hours. Marilyn mows the same lawn in 5 hours. How long will it take them to mow the lawn together?

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4 Answers

You can look at this as a rate problem. Jack takes 3 hours to cut one lawn and Marilyn takes 5 hours to cut one lawn. Another way of saying this is that Jack cuts 1/3 lawn per hour and Marilyn cuts 1/5 lawn per hour. If they work together you can combine those rates and get 1/3 + 1/5 = 5/15 + 3/15 = 8/15 lawn per hour together. 1 lawn divided by 8/15 lawns per hour is the same as 1 lawn times 15/8 hours/lawn =15/8 hours which is 1 7/8 hours total time if Jack and Marilyn work together. 
Here is another way to look at the problem.
Find the LCM of 3 and 5 which is 15.
In 15 hours Jack mows 5 lawns and Marilyn mows 3 lawns.
In 15 hours they mow 8 lawns.
15 hours/8 lawns= 1 7/8 hours per lawn
Hi Brooke;
Jack usually mows his lawn in 3 hours. Marilyn mows the same lawn in 5 hours. How long will it take them to mow the lawn together?
 
Jack moves 1/3 of the lawn in one hour.
Marilyn mows 1/5 of the lawn in one hour.
x=quantity of hours
 
[(1/3)+(1/5)]x=1
Let's eliminate annoying fractions.  (3)(5)=15  Therefore, let's multiply both sides by 15...
15[(1/3)+(1/5)]x=(1)(15)
(5+3)x=15
8x=15
Divide both sides by 8...
(8x)/8=15/8
x=15/8
x=1 7/8
x=1.875
It will require 1.875, 1 7/8, hours for both Jack and Marilyn to mow the lawn.
 
the best method to calculate this is to take 1lawn per 3hours and add 1lawn per 3 hours and determine the amount of lawns they could both do. then reduce to one lawn. this should give you 1.875 hours or 1 7/8 hours.