Middle School

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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 both worked together?

Answer :

Answer:

The time taken by both when they work together is 2 hours 42 minutes .

Step-by-step explanation:

Given as :

The time taken by Ryan to dig 10 ft by 10 ft hole = x = 5 hours

The time taken bu Castel to dig 10 ft by 10 ft hole = y = 6 hours

Let The time taken by both when they work together = z hours

According to question

The time taken by both when they work together = time taken by Ryan to dig 10 ft by 10 ft hole + time taken bu Castel to dig 10 ft by 10 ft hole

i.e [tex]\dfrac{1}{z}[/tex] = [tex]\dfrac{1}{x}[/tex] + [tex]\dfrac{1}{y}[/tex]

Or, [tex]\dfrac{1}{z}[/tex] = [tex]\dfrac{1}{5}[/tex] + [tex]\dfrac{1}{6}[/tex]

Taking LCM

Or, [tex]\dfrac{1}{z}[/tex] = [tex]\dfrac{6 + 5}{30}[/tex]

Or, [tex]\dfrac{1}{z}[/tex] = [tex]\dfrac{11}{30}[/tex]

Or, z = [tex]\dfrac{30}{11}[/tex] hours

∴ z = 2 hours 42 minutes

So, The time taken by both when they work together = z = 2 hours 42 min

Hence, The time taken by both when they work together is 2 hours 42 minutes . Answer

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Rewritten by : Barada