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Bunuel
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
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When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed, then

I found this question to be interesting and wanted to provide a simpler solution to this. I derived this question from the forum quiz, ultimately I was not able to answer <2 minutes but I knew I had the answer at the back of my mind.

I found that deriving Jack's Rate per Hour vs Mac's Rate per Hour to be the easiest way to understand this question.

3 x Jack's Rate x 2 Hour = Y + 10 pounds of olives
4/5 x Mac's Rate x 5 Hour = Y pounds of olives


Now let's analyse Jack's Rate and understand how fast his normal picks per hour is.

3 x Jack's Rate x 2 Hour = Y + 10 pounds of olives
3 x Jack's Rate = Y + 10 / 2
Jack's Normal Rate = Y + 10 / 6

4/5 x Mac's Rate x 5 Hour = Y pounds of olives
4/5 x Mac's Rate = Y / 5
Mac's Normal Rate = Y / 4

Now substitute the variables given 'Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed, then'

Jack's New Rate:
= ( Y + 10 / 6 ) x (3/4) x (4)
= (Y / 2) + 5

Mac's New Rate:
= (Y / 4) x 2
= (Y / 2)

Jack's New Rate vs Mac's New Rate
(Y / 2) + 5 - (Y / 2) = 5

Hope this helps everyone understand this better.­
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Let , Jack picks = x pounds / hour
In 2 hours with 3x pounds / hour , total = 6x pounds / hr

Mack picks = y pounds/hour
total he picks = 4/5y * 5 = 4y pounds / hour

Now , 6x = 4y + 10
3x - 2y = 5

Think of values which may work for this equation ,
x= 3 and y=2
Now ,
2y + 4 * (3/4x) = 4 + 9 ( SUbstituting x= 3 and y=2)

Mack picks 4 pounds and jack picks 9 pounds .

Option E is the naswer
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