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 olivesNow 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.