Question

Working alone Ryan can dig a 10ft by 10ft hole in five hours castel can dig the same same hole in six how long would it take them if they both worked together

Answer 1

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

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
`(1)/(z)` =
`(1)/(x)` +
`(1)/(y)`

Or,
`(1)/(z)` =
`(1)/(5)` +
`(1)/(6)`

Taking LCM

Or,
`(1)/(z)` =
`(6 + 5)/(30)`

Or,
`(1)/(z)` =
`(11)/(30)`

Or, z =
`(30)/(11)` 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