Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 10

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Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots.



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BTGmoderatorDC wrote:
Thu Feb 25, 2021 3:43 pm
Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots
Question stem, rephrased:
Is Tom slower than Matt?

Statement 1:
Case 1: Matt produces 1 pot in 1 hour, with the result that Matt's rate = work/time = 1/1 = 1 pot per hour
Since Tom takes 4 more hours to produce twice the number of pots, Tom takes 5 hours to produce 2 pots, with the result that Tom's rate = work/time = 2/5 pot per hour.
In this case, Tom is SLOWER than Matt, so the answer to the rephrased question stem is YES.

Case 2: Matt produces 10 pots in 10 hours, with the result that Matt's rate = work/time = 10/10 = 1 pot per hour
Since Tom takes 4 more hours to produce twice the number of pots, Tom takes 14 hours to produce 20 pots, with the result that Tom's rate = work/time = 20/14 = 10/7 pots per hour
In this case, Tom is FASTER than Matt, so the answer to the rephrased question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2:
If Tom and Matt were to work at the same rate, Tom would take 3 times as long as Matt to produce 3 times the number of pots.
Since Tom only takes TWICE as long as Matt to produce 3 times the number of pots, Tom must be FASTER than Matt.
Thus, the answer to the rephrased question stem is NO.
SUFFICIENT.

The correct answer is B.
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