Question

It takes Carl 8 hours to plant his garden, but only 6 hours if his son helps him. How long would it take his son to plant the garden alone?

Answer 1

24 hours

Explanation:

Let t represent time taken by Carl's son to complete the work alone.

Part of garden planted by Carl's son in 1 hour would be
`(1)/(t)`.

We have been given that Carl can plant his garden in 8 hours, so part of garden planted by Carl in 1 hour would be
`(1)/(8)`.

We have been given that Carl can plant his garden in 6 hours with his son, so part of garden planted by Carl and his son in 1 hour would be
`(1)/(8)+(1)/(t)=(1)/(6)`.

Now, let us solve for t.

`(1)/(8)-(1)/(8)+(1)/(t)=(1)/(6)-(1)/(8)`

`(1)/(t)=(1)/(6)-(1)/(8)`

Make a common denominator:

`(1)/(t)=(1*4)/(6*4)-(1*3)/(8*3)`

`(1)/(t)=(4)/(24)-(3)/(24)`

`(1)/(t)=(4-3)/(24)`

`(1)/(t)=(1)/(24)`

Cross multiply:

`1t=1*24`

`t=24`

Therefore, it will take Carl's son 24 hours to plant the garden alone.

Answer 2

Answer: 24 hours

Explanation:

Given : Time taken by Carl to plant his garden alone = 8 hours

If his son helps him , then the time taken by them = 6 hours

Let t be the time taken by son to plant the garden alone , then we have the following equation :-

`(1)/(6)=(1)/(t)+(1)/(8)\\\\\Rightarrow(1)/(t)=(1)/(6)-(1)/(8)\\\\\Rightarrow(1)/(t)=(4-3)/(24)=(1)/(24)\\\\\Rightarrow\ t=24`

Hence, the son will take 24 hours to plant the garden alone.