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

hi sunita123,
you are absolutely correct in that front..
i mean by couples one hour work=1/1+1/2=3/2 that the couple can finish 3/2 times of work in one hour ..
so they can finish the work in 2/3 hrs

sunita123
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Here's how you can solve the doubt you've:

Work-Rate problems are inverse proportion type situations ie More men - Less time required (Hence, inversely proportional)

Man and Wife do work together - in 1 hour how much can both do? So in 1 hr man can finish the whole job and wife can finish half the job right?
Look at this in terms of efficiency i.e. Man has 100% efficiency in 1 hour and wife has efficiency of 50% in 1 hour. -> Combined their efficieny becomes 150%

More efficiency -> more work done -> less time taken

Note:
Relating efficiency to 1 unit of time and work: if a man takes 'n' hours or 'n' days to finish his task, then his efficiency must be measured in terms of each of the individual hours of 'n' hours or each of the days counted in 'n' days. For eg: woman takes 2 hours to complete task implies her efficiency in 1 hour is 50% giving efficiency in 2 hrs to be 100%; in mathematial form:

W takes 2 hours > in 1 hour she does 1/2 of work > efficiency 1/2 X 100 = 50% > in two hours 2 X (1/2) X 100 > giving us 2 hrs (100% efficiency) > basically the inverse of 1/n (here 1/2) gives how much time she takes to do the full job > 2 hrs.

So now going back to problem: M and W's total efficiency is 150% - 150/100 > inverse > 100/150 = 2/3 (why inverse? because they dont have to finish 1.5 amount of job. They've to finish 1W not 1.5W so unitary method approach applied here )

For kids > 1/4+1/6 = 5/12 > inverse = 12/5

Ratio > (2/3)/(12/5) = 5:18

Hope this helps

Work-rate problems can also be looked at in the same form as the Distance = Speed X time, where we replace Distance by Work and Speed by rate.

For example, in this problem, Work = Rate X Time, where Work = 1 unit, Rate of Husband = \(R_H\)=1/1 (as Work is 1 unit and time husband takes = 1 hour).

Similarly, Rates of Wife, Rae and Herman are : \(R_W\)=1/2, \(R_R\)=1/4 and \(R_{He}\)=1/6

Now, for combined rates, \(R_H\)+\(R_W\)=1+1/2 = 3/2 (we are adding the rates here as the more efficient or high the rates are the sooner will be work be finished. It is very similar to if the speed is higher, you will take less time to cover the same distance!)

and \(R_R\)+\(R_He\) = 1/4+1/6 = 10/24

Thus, time taken by Husband and Wife to do 1 unit of work, 1 = 3/2*\(t_1\)

>> \(t_1\)=2/3 hours

Time taken by Rae and Herman to do 1 unit of work , 1 = 10/24*\(t_2\)

>> \(t_2\)= 24/10 hours

Finally, \(\frac{t_1}{t_2}\) = (2/3)/(24/10)= \(\frac{5}{18}\)

Thank you everyone for the explanation:). this certainly helps.

Hi All,

This prompt can also be solved by using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual times that it takes to complete the 'job'

We're told that a husband and wife can complete a task in 1 hour and 2 hours, respectively. Working together, it would take them...

(1)(2)/(1+2) = 2/3 hours to complete the task

Next, we're told that the two children can complete the task in 4 hours and 6 hours, respectively. Working together, it would take them...

(4)(6)/(4+6) = 24/10 hours to complete the task

We're asked for the RATIO of the couple's time to the children's time....

(2/3) / (24/10) =
(2/3)(10/24) =
20/72 =
5/18

Final Answer:

GMAT assassins aren't born, they're made,
Rich

We know work done together:

\(\frac{ab}{a + b}\)

For Husband and Wife we can write:

\(\frac{1}{1} + \frac{1}{2} = 2 * \frac{1}{2} + 1 = \frac{2}{3}\)

For Rae and Herman we can write:

\(\frac{1}{4} + \frac{1}{6} = \frac{24}{10} = \frac{12}{5}\)

So, ratio of couple and children working together:

\(= \frac{2/3}{12/5}\)

\(= \frac{2}{3} * \frac{5}{12}\)

\(= \frac{5}{18}\)

\(= 5:18\)

Hence, Answer is D

Hello Rich,

Thanks for the explaination. How could we solve this problem by assuming values for work?

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