Question

It takes Hank 40 minutes (2/3 hours) to mow a lawn. Penny can mow the same size lawn in 30 minutes (1/2 hour). Hank and Penny form a small lawn care company and have contracts for 7 lawns of the same size previously mentioned. How long should it take both of them working together to mow the 7 lawns? (Hint: find a combined hourly rate of ""lawns per hour"" for Hank and Penny

Answer 1

2 hours

Explanation:

Given: It takes Hank
`40` minutes
`(2)/(3)` hours to mow a lawn. Penny can mow the same size lawn in
`30` minutes
`(1)/(2)` hours. Hank and Penny form a small lawn care company and have contracts for
`7` lawns of the same size previously mentioned.

To Find: How long should it take both of them working together to mow the
`7` lawns.

Solution:

Time taken by Hank to mow the lawn
`=(2)/(3)`
`\text{hour}`

Time taken by Penny to mow the lawn
`=(1)/(2)`
`\text{hour}`

Total lawns to be mowed
`=7`

Let time taken by Hank and Penny to mow one lawn
`=\text{T}`

`\frac{1}{\text{time taken by Hank}}+\frac{1}{\text{time taken by Penny}}=\frac{1}{\text{Time taken by both to mow one lawn}}`

`(1)/((2)/(3))+(1)/((1)/(2))=\frac{1}{\text{T}}`

`(7)/(2)=\frac{1}{\text{T}}`

`\text{T}=(2)/(7)`

time taken to mow
`7` lawns
`=7*\text{time taken to mow one lawn}`

`=7*(2)/(7)`

`=2`
`\text{hour}`

Hence it will take
`2`
`\text{hours}` by Hank and Penny to mow
`7` lawns