Question

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?

Answer 1

`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.

Answer 2

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]