Question

Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Castel can dig the same while in six hours. How long would it take them if they worked together?

Answer 1

Answer:

$2\frac{8}{11}$ hours.

Step-by-step explanation:

Let t represent time taken in hours by both working together.

So part of work completed by working together in 1 hour would be $\frac{1}{t}$.  

We have been given that working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. So part of work completed by Ryan in 1 hour would be $\frac{1}{5}$.

We are also told that Castel can dig the same while in six hours. So part of work completed by Castel in 1 hour would be $\frac{1}{6}$.

Since they will work together, so we can equate sum of work completed by both as:

$\frac{1}{t}=\frac{1}{6}+\frac{1}{5}$

$\frac{1}{t}\times 30t=\frac{1}{6}\times 30t+\frac{1}{5}\times 30t$

$30=5t+6t$

$30=11t$

$11t=30$

$\frac{11t}{11}=\frac{30}{11}$

$t=2\frac{8}{11}$

Therefore, it will take $2\frac{8}{11}$ hours to dig the pool working together.