Answer: it will take them 2 hours to now 7 lawns
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