Question

They could mow the lawn in how many hours if they work together

Answer 1

Hello!

First, figure out their mowing rates per hour.

Jack's is
`(1)/(3)` since he mows 1 lawn in 3 hours; Marilyn's is
`(1)/(7)` since she mows 1 lawn in 7 hours.

We now know that their combined rate of mowing 1 lawn is
`(1)/(3) + (1)/(7)`. Use the variable t for time and multiply it by their combined rate to figure out their combined time of mowing 1 lawn.


`( (1)/(3) + (1)/(7))t =1`


`( (7)/(21) + (3)/(21) )t=1`


`(10)/(21) t =1`


`t= (21)/(10)`

Answer:
Jack and Marilyn could mow the lawn in
`(21)/(10)` or 2.1 hours if they work together.

Answer 2

As Jack can mow the yard 7/3 Times faster than Marilyn , Jack can mow 70% of the yard while Marilyn can mow 30% of the yard in the same time Jack would mow 70%.

Jack can mow 10% of the yard in 0.3 hours
Marilyn can mow 10% of the yard in 0.7 hours

Jack will mow 70% of the yard : 0.3 hours ( 10% ) × 7
= 2.1 hours . Jack can mow 70% of the yard in 2.1 hours

Marilyn will mow 30% of the yard : 0.7 hours ( 10%) × 3 = 2.1 hours. Marilyn can mow 30% of the yard in 2.1 hours.

John mowwing for 2.1 hours + Marilyn mowwing for 2.1 hours = 100% of the yard in 4.2 hours.

Awnser : 4.2 hours