Question

Working alone it would take laura 45 minutes to mow the lawn kelly would take 1 hour 15 minutes if they work together the girls believe it will take 1 hour to mow the lawn which is the best described of the solution

Answer 1

31.5 minutes only

Inverse proportion

Explanation:

It takes 45 minutes for Laura to mow the lawn.

For Kelly it takes 1 hour 45 minutes or 60+45 = 105 minutes

In one minute Laura can mow 1/45 of the lawn.

Similarly in one minute Kelly can mow 1/105 of the lawn

Together in one minute they can mow the sum

=
`(1)/(45) +(1)/(105)`

Take lcd for 45 and 105 and make them equivalent fractions with same denominator

LCD of 45 and 105 is 15(3) (7) = 315

`(1)/(45) +(1)/(105)=(7+3)/(315)=(10)/(315)\\=(2)/(63)`

In other words it would take 63/2 = 31.5 minutes only to lawn if they work together.

The situation here is the problem on inverse proportion. If no of people increase, work time would decrease.