Question

1. working alone joe can cut his grass in 45 minutes and his wife mary can cut the grass in 30 minutes. joe started cutting his grass and 10 minutes later his wife joined him. how long will it take them to finish cutting the grass after his wife joined.

Explanation:

Step1: Define work rates

Let the total work (cutting the grass) be 1. Joe's rate: $\frac{1}{45}$ per minute. Mary's rate: $\frac{1}{30}$ per minute.

Step2: Work done by Joe alone

Joe works 10 minutes alone. Work done: $10\times\frac{1}{45}=\frac{2}{9}$.

Step3: Remaining work

Remaining work: $1 - \frac{2}{9}=\frac{7}{9}$.

Step4: Combined rate of Joe and Mary

Combined rate: $\frac{1}{45}+\frac{1}{30}=\frac{2 + 3}{90}=\frac{5}{90}=\frac{1}{18}$ per minute.

Step5: Time to finish remaining work

Let $t$ be time to finish remaining work. $\frac{1}{18}t=\frac{7}{9}$. Solve: $t=\frac{7}{9}\times18 = 14$ minutes.

Answer:

14 minutes