I30-37

Question

Olivia, Jacob, and Ethan are laying down tile flooring in a large hallway. Working alone at their respective rates, Olivia can tile the hallway in 6 hours, Jacob can tile the hallway in 4 hours, and Ethan can tile the hallway in 5 hours. To speed up the work, exactly two of them will work together to tile the hallway.
 
Select for  Shortest Time  the time closest to the least amount of time required for any 2-person team to complete the hallway, and select for  Longest Time  the time closest to the greatest amount of time required for any 2-person team to complete the hallway. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Individual rates:
 
• Olivia — 1/6 hallway per hour
 
• Jacob — 1/4 hallway per hour
 
• Ethan — 1/5 hallway per hour
 
 Fastest pair is Jacob and Ethan. 
 
• Combined rate = 1/4 + 1/5 = 9/20 hallway per hour
 
• Time = 1/(9/20) = 20/9 hours
 
• 20/9 hours = 2 hours and 2/9 of an hour
 
• 2/9 * 60 minutes ≈ 13 minutes
 
So, time ≈ 2 hours 13 minutes
 
 Slowest pair is Olivia and Ethan. 
 
• Combined rate = 1/6 + 1/5 = 11/30 hallway per hour
 
• Time = 1/(11/30) = 30/11 hours
 
• 30/11 hours = 2 hours and 8/11 of an hour
 
• 8/11 * 60 minutes ≈ 44 minutes
 
So, time ≈ 2 hours 44 minutes

Correct answer:

Shortest Time  "2 hours 13 minutes"

Longest Time  "2 hours 44 minutes"

sb995 · Answer

I did not quite understand the solution. Is there any way to use logic to solve this instead of solving algebraically? Thank you.

Bunuel · Answer

Check alternative solutions here: https://gmatclub.com/forum/olivia-jacob ... 35533.html Hope it helps.

I30-37

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My Rewards

Shortest Time	Longest Time
		2 hours 2 minutes
		2 hours 9 minutes
		2 hours 13 minutes
		2 hours 44 minutes
		2 hours 54 minutes