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: it will take them 2 hours to now 7 lawns

Step-by-step explanation:

It takes Hank 40 minutes (2/3 hours) to mow a lawn. This means that his unit rate of working is 1/40

Penny can mow the same size lawn in 30 minutes (1/2 hour). This means that his unit rate of working is 1/30

If they form a small lawn care company, they will be working together and simultaneously at a faster combined rate. Since their rates are additive.

If they finish one lawn in t hours, working together, then their combined working rate for one lawn is 1/t. Therefore

1/40 + 1/30 = 1/t

1/t = 7/120

t = 120/7 = 17.14

They will now one lawn in 17.14 minutes

For 7 lawns, it will take them 17.14 × 7 = 119.98 minutes. It is approximately 120 minutes.

We will convert from minutes to hour.

60 minutes = 1 hour

120 minutes = 120/60 = 2 hours