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

Answer:

The correct option is D) 5:18.

Step-by-step 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:

$\frac{1}{1}+\frac{1}{2}=\frac{3}{2}$

Thus, the work done is:$\frac{2}{3}$

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:

$\frac{1}{4}+\frac{1}{6}=\frac{5}{12}$

Thus, the work done is:$\frac{12}{5}$

Now calculate the ratio as shown.

$Ratio=\frac{\frac{2}{3}}{\frac{12}{5}}$

Ratio=5:18

Hence, the required ratio is 5:18.

Thus the correct option is D) 5:18.

Answer 2

Answer:

5:18

Step-by-step 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 $\frac{1}{2}$

When both work together then the rate of work done is $1+\frac{1}{2}=\frac{3}{2}$

So when they work together they need $\frac{1}{\frac{3}{2}}=\frac{2}{3}\ hour$

It is given that Rae can complete the work in 4 hopur so rate of work done of Rae is $\frac{1}{4}$

It is also given that Herman can complete the work in 6 hour so rate of work done of Herman is $\frac{1}{6}$

If both children work together then their rate of work done is $\frac{1}{6}+\frac{1}{4}=\frac{5}{12}$

So when they work together they need $\frac{1}{\frac{5}{12}}=\frac{12}{5}\ hour$

So the ratio of couple's time working together to the children's time working together is $\frac{\frac{\frac{2}{3}}{12}}{5}=\frac{5}{18}$