Question

jamie can cut the lawn in 45 minutes. her sister jessica can cut the lawn in 35 minutes. is it reasonable for the two of them working together to cut the lawn in less than 25 minutes?
a yes, the time will be about 15 minutes.
b yes, the time will be about 20 minutes.
c no, the time would be about 30 minutes.
d no, the time would be about 40 minutes.

Explanation:

Step1: Define work rates

Jamie's rate: $\frac{1}{45}$ lawn per minute
Jessica's rate: $\frac{1}{35}$ lawn per minute

Step2: Combine work rates

Combined rate = $\frac{1}{45} + \frac{1}{35}$
Find common denominator (315):
$\frac{7}{315} + \frac{9}{315} = \frac{16}{315}$ lawn per minute

Step3: Calculate total time

Time = $\frac{1}{\text{Combined rate}} = \frac{315}{16} = 19.6875$ minutes

Step4: Compare to 25 minutes

19.6875 minutes < 25 minutes, so it is reasonable.

Answer:

B. Yes, the time will be about 20 minutes.