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

Answer :

Answer:

[tex]2\frac{8}{11}[/tex] 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 [tex]\frac{1}{t}[/tex].

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 [tex]\frac{1}{5}[/tex].

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 [tex]\frac{1}{6}[/tex].

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

[tex]\frac{1}{t}=\frac{1}{6}+\frac{1}{5}[/tex]

[tex]\frac{1}{t}\times 30t=\frac{1}{6}\times 30t+\frac{1}{5}\times 30t[/tex]

[tex]30=5t+6t[/tex]

[tex]30=11t[/tex]

[tex]11t=30[/tex]

[tex]\frac{11t}{11}=\frac{30}{11}[/tex]

[tex]t=2\frac{8}{11}[/tex]

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

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Rewritten by : Barada