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A husband and his wife

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Source: — Problem Solving |

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by [email protected] » Mon Feb 15, 2016 11:20 pm
Hi didieravoaka,

This question can be solved using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the two times that it takes two individuals to complete a task.

Here, we're told that two parents can complete a task in 1 and 2 hours, respectively. Working together, they can complete the task in...

(1)(2)/(1+2) = 2/3 of hour to complete the task when working together

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

(4)(6)/(4+6) = 24/10 = 12/5 hours to complete the task when working together.

We're asked for the ratio of the parent's time to complete the task to the children's time to complete the task...

(2/3) : (12/5) =
(10/15) : (36/15) =
10 : 36 =
5 : 18

Final Answer: D

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by MartyMurray » Tue Feb 16, 2016 4:57 am
didieravoaka wrote:A husband and wife can complete a certain task in 1 and 2 hours respectively. Their childred, 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?

(A) 15:46

(B) 3:10

(C) 12:23

(D) 5:18

(E) 10:3
Here's the most basic way to solve it, one that you can apply to answering pretty much any work and rate question.

Calculate the rates of each person.

Husband: 1 task per hour

Wife: 1/2 task per hour

Rae: 1/4 task per hour

Herman: 1/6 task per hour

Combine the rates and calculate the times of the duos.

Husband and Wife complete 3/2 tasks per hour.

So one task will take them 2/3 of an hour.

Rae and Herman complete 1/4 + 1/6 = 6/24 + 4/24 = 10/24 = 5/12 of a task per hour.

So one task will take them 12/5 of an hour.

Find the ratio of the two times.

2/3:12/5 = 1/3:6/5 = 5:18

The correct answer is D.
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by GMATGuruNY » Tue Feb 16, 2016 5:52 am
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?

a)15:46

b)3:10

c)12:23

d)5:18

e)10:3
Let the task = the LCM of 1, 3, 4 and 6 = 12 widgets.

Since the husband takes 1 hour to complete the task, the husband's rate = w/t = 12/1 = 12 widgets per hour.
Since the wife takes 2 hours to complete the task, the wife's rate = w/t = 12/2 = 6 widgets per hour.
Combined rate for the husband and wife = 12+6 = 18 widgets per hour.

Since Rae takes 4 hours to complete the task, Rae's rate = w/t = 12/4 = 3 widgets per hour.
Since Herman takes 6 hours to complete the task, Herman's rate = w/t = 12/6 = 2 widgets per hour.
Combined rate for Rae and Herman = 3+2 = 5 widgets per hour.

Rate and time have a RECIPROCAL RELATIONSHIP:
3 times as fast implies 1/3 the time.
1/2 the time implies twice the rate.

The RATE RATIO for the adults and children = (18 widgets per hour) : (5 widgets per hour).
Thus, the TIME RATIO is equal to the reciprocal:
(5 hours) : (18 hours).

The correct answer is D.
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by didieravoaka » Tue Feb 16, 2016 2:49 pm
Thanks to all of you guys. Each of your answers are really good.
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