Hi All,
This question can be solved by TESTing THE ANSWERS.
We're given rates for Machine P (30 gallons/minute) and Machine Q (45 gallons/minute) and we're told how long it would take each machine to finish a job (6 hours and 4 hours respectively). We can use this information to figure out the TOTAL JOB....
Total Job = (30 gallons/min)(60 mins)(6 hours) = 10,800 Gallons
We're then given a specific set of circumstances to calculate: Machine Q works by itself for a period of time, then the two machine work together for the SAME amount of time that Machine Q worked by itself. We're told that this situation will complete the entire job. We're asked how long it would take to complete the job under these circumstances.
Logically, since Machine Q can do the entire job on its own in 4 hours, with the added help of Machine P, the amount of time MUST be LESS than 4 hours.
Let's TEST Answer B....
If the Total job was 3 hours, then Machine Q would work for 1.5 hours by itself, then Machines P and Q would work for another 1.5 hours together. We can now calculate how many Gallons are processed in this situation...
Machine Q = (45 gallons/min)(90 minutes) = 4,050 gallons
Machines P+Q = (45+30 gallons/min)(90 minutes) = 6,750 gallons
Total = 4,050 + 6,750 = 10,800 gallons.
This IS the exact TOTAL we are supposed to end up with, so the total time MUST be 3 hours.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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