Question #f19cb
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The time it would take for Jack and Marilyn to mow the lawn together will be #2#hours and #55# minutes.
Jack mows the lawn in #5# hours.
That means Jack mows #1/5# th of the lawn in #1 # hour.
Similarly,
Marilyn can mow the same lawn in #7 #hours.
That means, Marilyn mows #1/7# th of the lawn in #1# hour.
So if they work together,
In 1 hour they will mow #1/5 +1/7 # th of the lawn, i.e.:
#=1/5(7/7) + 1/7(5/5)#
#= 7/35+5/35 = 12/35#th of the lawn is mowed in #1# hour.
That means, they will need #35/12# hours to mow the lawn together,i.e.:
#35/12 = 2 11/12# hours.
#11/12#th of an hour =# 11/12 x 60# minutes= #55# minutes.
The time it would take for Jack and Marilyn to mow the lawn together will be #2#hours and #55# minutes.
In #5# hrs Jack mows #1# Lawn
So in #1# hr Jack mows #1/5# Lawn
In #7# hrs Marilyn mows #1# Lawn
So in #1# hr Marilyn mows #1/7# Lawn
So we can write together Jack and Marilyn in #1# hr can mow #1/5+1/7=(7+5)/35=12/35# Lawn
So they can mow a Lawn i.e. #1# Lawn in #35/12 hrs=2 11/12hrs#=#2hrs# #55 minutes#
