Respuesta :
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:
[tex]\frac{1}{1}+\frac{1}{2}=\frac{3}{2}[/tex]
Thus, the work done is:[tex]\frac{2}{3}[/tex]
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:
[tex]\frac{1}{4}+\frac{1}{6}=\frac{5}{12}[/tex]
Thus, the work done is:[tex]\frac{12}{5}[/tex]
Now calculate the ratio as shown.
[tex]Ratio=\frac{\frac{2}{3}}{\frac{12}{5}}[/tex]
Ratio=5:18
Hence, the required ratio is 5:18.
Thus the correct option is D) 5:18.
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 [tex]\frac{1}{2}[/tex]
When both work together then the rate of work done is [tex]1+\frac{1}{2}=\frac{3}{2}[/tex]
So when they work together they need [tex]\frac{1}{\frac{3}{2}}=\frac{2}{3}\ hour[/tex]
It is given that Rae can complete the work in 4 hopur so rate of work done of Rae is [tex]\frac{1}{4}[/tex]
It is also given that Herman can complete the work in 6 hour so rate of work done of Herman is [tex]\frac{1}{6}[/tex]
If both children work together then their rate of work done is [tex]\frac{1}{6}+\frac{1}{4}=\frac{5}{12}[/tex]
So when they work together they need [tex]\frac{1}{\frac{5}{12}}=\frac{12}{5}\ hour[/tex]
So the ratio of couple's time working together to the children's time working together is [tex]\frac{\frac{\frac{2}{3}}{12}}{5}=\frac{5}{18}[/tex]
