Question

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

Answer 1

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

Answer 2

Hello!

First, figure out their mowing rates per hour.

Jack's is $\frac{1}{3}$ since he mows 1 lawn in 3 hours; Marilyn's is $\frac{1}{7}$ since she mows 1 lawn in 7 hours.

We now know that their combined rate of mowing 1 lawn is $\frac{1}{3} + \frac{1}{7}$. Use the variable t for time and multiply it by their combined rate to figure out their combined time of mowing 1 lawn.

$( \frac{1}{3} + \frac{1}{7})t =1$

$( \frac{7}{21} + \frac{3}{21} )t=1$

$\frac{10}{21} t =1$

$t= \frac{21}{10}$

Answer:
Jack and Marilyn could mow the lawn in $\frac{21}{10}$ or 2.1 hours if they work together.