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18 Jan 2019, 01:10
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
78% (02:14) correct
22%
(02:34)
wrong
based on 216
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Working alone at a constant rate, Machine A can produce 15 widgets in 2 minutes. Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes. If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?
A 12
B 24
C 36
D 48
E 60
A 12
B 24
C 36
D 48
E 60
18 Jan 2019, 20:26
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Working alone at a constant rate, Machine A can produce 15 widgets in 2 minutes.
Machine A rate: \(\frac{15 (widgets)}{2 (minutes)}\)
Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes.
Machine B rate:\(\frac{20 (widgets)}{3 (minutes)}\)
If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?
rate·time=work completed
We have the respective rates from above.
Machine A and B both work for the same time (we'll denote this time with x).
We know the work completed is a difference of 40
Machine A Rate·x - Machine B Rate·x=40 widgets
\(\frac{15 (widgets)}{2 (minutes)}·x - \frac{20 (widgets)}{3 (minutes)}·x=40 (widgets)\)
eliminate units for simplicity. Just remember x will be units of time
\(\frac{15x}{2}-\frac{20x}{3}=40\)
\(\frac{45x}{6}-\frac{40}{6}=40\)
\(\frac{5x}{6}=40\)
5x=240
x=48 minutes
D
Machine A rate: \(\frac{15 (widgets)}{2 (minutes)}\)
Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes.
Machine B rate:\(\frac{20 (widgets)}{3 (minutes)}\)
If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?
rate·time=work completed
We have the respective rates from above.
Machine A and B both work for the same time (we'll denote this time with x).
We know the work completed is a difference of 40
Machine A Rate·x - Machine B Rate·x=40 widgets
\(\frac{15 (widgets)}{2 (minutes)}·x - \frac{20 (widgets)}{3 (minutes)}·x=40 (widgets)\)
eliminate units for simplicity. Just remember x will be units of time
\(\frac{15x}{2}-\frac{20x}{3}=40\)
\(\frac{45x}{6}-\frac{40}{6}=40\)
\(\frac{5x}{6}=40\)
5x=240
x=48 minutes
D
General Discussion
Archit3110
Major Poster
18 Jan 2019, 08:09
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Bunuel
rate for A = 15/2
rate for B = 20/3
solve using answer options we see
that at 48 mins ; A would have made 40 more widgets than B
15*48/2 = 360
20*48/3 = 320
IMO D
