Question

A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task? 15 : 46 3 : 10 12 : 23 5 : 18 10 : 3

Answer 1

5:18

Explanation:

Husband can complete the task in 1 hour so rate of husband work done is 1

Wife can complete the task in 2 hour so the rate of work done of wife is
`(1)/(2)`

When both work together then the rate of work done is
`1+(1)/(2)=(3)/(2)`

So when they work together they need
`(1)/((3)/(2))=(2)/(3)\ hour`

It is given that Rae can complete the work in 4 hopur so rate of work done of Rae is
`(1)/(4)`

It is also given that Herman can complete the work in 6 hour so rate of work done of Herman is
`(1)/(6)`

If both children work together then their rate of work done is
`(1)/(6)+(1)/(4)=(5)/(12)`

So when they work together they need
`(1)/((5)/(12))=(12)/(5)\ hour`

So the ratio of couple's time working together to the children's time working together is
`(((2)/(3))/(12))/(5)=(5)/(18)`

Answer 2

The correct option is D) 5:18.

Explanation:

Consider the provided information.

A husband and wife can complete a certain task in 1 and 2 hours respectively.

Then in 1 hr the work done by the husband and wife is:

`(1)/(1)+(1)/(2)=(3)/(2)`

Thus, the work done is:
`(2)/(3)`

Rae and Herman, can complete the same task in 4 and 6 hours, respectively.

Then in 1 hr the work done by Rae and Herman is:

`(1)/(4)+(1)/(6)=(5)/(12)`

Thus, the work done is:
`(12)/(5)`

Now calculate the ratio as shown.

`Ratio=((2)/(3))/((12)/(5))`

Ratio=5:18

Hence, the required ratio is 5:18.

Thus the correct option is D) 5:18.