Jack usually mows his lawn in 4 hours. Marilyn can mow the same yard in 3 hours. How much time would it take for them to mow the lawn together?

2 Answers
Mar 30, 2017

#12/7# hours

Explanation:

Since Jack takes #4# hours. to mow his lawn, he mows #1/4# of his lawn each hour. Since Marilyn takes #3# hours., he mows #1/3# of the same lawn each hour.

Suppose that they spend #t# hours working together mowing the lawn. Jack can get #t/4# of his lawn done, and Marilyn can get #t/3# of his lawn done. In total, #t/4+t/3# is done.

When they finish, exactly #1# of the lawn is done. In other words, #t/4+t/3=1#. We combine the left-hand side into one fraction: #(7t)/12=1#. Solving for #t#, we get #t=12/7# hours.

Mar 30, 2017

Jack and Marilyn together will take #1 5/7# hour to mow the lawn.

Explanation:

Jack mows his lawn in #4# hours.
So in #1# hour Jack mows #1/4#th of his lawn.

Marilyn mows same lawn in #3# hours.
So in #1# hour Marylin mows #1/3#rd of the lawn.

So in #1# hour both together will mow #1/4+1/3= 7/12# part of the lawn.
Therefore, they both together will take # 1/(7/12) = 12/7 = 1 5/7# hour to mow the lawn. [Ans]