Question

Working alone, it takes Brenda 14 hours to pick 40 apples. Ted can pick up the same amount in 12 hours. Find how long it would take them if they worked together

Answer 1

6.5 hours to the nearest tenth

Explanation:

Brenda takes 14 hours to pick 40 apples, so her rate is
`(1)/(14)`

Ted can also pick 40 apples in 12 hours, Ted's rate is
`(1)/(12)`

The combined rate of Brenda and Ted is
`(1)/(14)+(1)/(12)`...eqn1

Let
`y` represent how long it would take if they worked together.

Their rate of working together in terms of y is
`(1)/(y)`...eqn2

Equations (1) and (2) are equal.

This implies that:

`(1)/(y)=(1)/(14)+(1)/(12)`

`(1)/(y)=(13)/(84)`

`y=(84)/(13)=6.46}`

Therefore it would take approximately 6.5 hours if they work together