Question

working alone, it takes ashley five hours to pour a large concrete driveway. ming can pour the same driveway in eight hours. find how long it would take them if they worked together.

Explanation:

Step1: Define work rates

Let the total work (pouring the driveway) be \(1\) unit. Ashley's rate: \(\frac{1}{5}\) per hour (since she takes 5 hours alone). Ming's rate: \(\frac{1}{8}\) per hour (since she takes 8 hours alone).

Step2: Combined rate

Combined rate of Ashley and Ming: \(\frac{1}{5}+\frac{1}{8}\). Find a common denominator (40): \(\frac{8}{40}+\frac{5}{40}=\frac{13}{40}\) per hour.

Step3: Time to complete together

Let \(t\) be the time together. Work done: rate \(\times\) time = \(1\). So \(\frac{13}{40}t = 1\). Solve for \(t\): \(t=\frac{40}{13}\approx 3.08\) hours.

Answer:

\(\frac{40}{13}\) hours (or approximately \(3.08\) hours)