Question

HELP I HAVE TO FINISH IN 2 HOURS

shannon and sarah are mowing a field. shannon can finish mowing by herself in 2 hours. sarah can finish in 4 hours. how long will it take them to mow the field together?

Answer 1

4/3 hours

Explanation:

For every hour that Sarah mows, Shannon mows twice as much. Because of this, Sarah is going to mow two times as much of the field as Shannon. You can set up an equation where x is the fraction of lawn mowed. This equation should be:

2x + x = 1 -> 3x = 1

The reason the equation is set up like this is because there is 1 whole lawn that the fraction of the lawn that Shannon mows (2x) plus the fraction of the lawn that Sarah mows (x) adds up to. You can use this equation to solve for x, which will be 1/3.

Since you know x, you can find what fraction of the lawn Shannon and Sarah mow. Since Shannon mows a fraction of 2x of the lawn, the fraction she mows will be 2*1/3 = 2/3. The fraction that Sarah mows will be x = 1/3.

Now that you know the fraction of the whole lawn that both Saran and Shannon mow, you can multiply their respective fraction by the amount of time it takes for them to mow a whole lawn. To do this for Shannon, you multiply 2/3 of the lawn by 2 hours, which gives you 4/3 hours. To do this for Sarah, you multiply 1/3 of the lawn by 4 hours, which also gives you 4/3 hours.

Answer 2

1h 20m

Explanation:

Let the total amount of work be x.

Shannon:

2h = x

1h =
`(1)/(2)`x

So basically Shannon does
`(1)/(2)`x work per hour.

Sarah:

4h = x

1h =
`(1)/(4)`x

So basically Sarah does
`(1)/(4)`x work per hour.

Together:

1h =
`(1)/(2)`x +
`(1)/(4)`x

=
`(2)/(4)`x +
`(1)/(4)`x

=
`(3)/(4)`x

Amount of time spent =
`(4)/(4)`x ÷
`(3)/(4)`x

=
`(4)/(4)`x ×
`(4)/(3)`x

=
`(16)/(12)`h

= 1
`(4)/(12)`h

= 1h 20m