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

Answer:

2 hours

Step-by-step explanation:

Given: It takes Hank $40$ minutes $\frac{2}{3}$ hours to mow a lawn. Penny can mow the same size lawn in $30$ minutes $\frac{1}{2}$ 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 $=\frac{2}{3}$ $\text{hour}$

Time taken by Penny to mow the lawn $=\frac{1}{2}$ $\text{hour}$

Total lawns to be mowed $=7$

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

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

$\frac{1}{\frac{2}{3}}+\frac{1}{\frac{1}{2}}=\frac{1}{\text{T}}$

$\frac{7}{2}=\frac{1}{\text{T}}$

$\text{T}=\frac{2}{7}$

time taken to mow $7$ lawns $=7\times\text{time taken to mow one lawn}$

                                                   $=7\times\frac{2}{7}$

                                                   $=2$ $\text{hour}$

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