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10 Mar 2018, 14:53
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shash
Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes.
A. 2
B. 3
C. 4
D. 6
E. 60/7
A. 2
B. 3
C. 4
D. 6
E. 60/7
ptl0u1
Instead of 2.5 hours , 2 hours and (2/5) mins then answer will be 4 hours . Correct?
ptl0u1 , no, the answer is \(\frac{60}{7}\) hours.I'm not sure you worked from the right prompt, although your question seems to match. Are you asking about --rates? Where did you get (2/5 mins)? Could you quote the prompt you used?
A's rate = \(\frac{6,000}{3hrs} = \frac{2,000}{1hr}\)
\(A = 2,000\) per hour
\(B + C = \frac{6,000}{\frac{5}{2}hr}=6,000*\frac{2}{5}hr=\frac{2,400}{1hr}\)
\(B + C = 2,400\) per hour
\(A + C = 3,000\) per hour
Find C.
\(A + C = 3,000\)
\(A = 2,000\) =>
\(C = 1,000\)
Find B
\(B + C = 2,400\)
\(C = 1,000\) =>
\(B = 1,400\) per hour
Time for B to process 12,000 envelopes?
\(R*T = W\), so \(T =\frac{W}{R}\)
\(\frac{12,000}{1,400}=\frac{120}{14}=\frac{60}{7}\) hrs
Answer E
Hope that helps.
20 Nov 2021, 23:33
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I took a longer approach, but an easier one-
A took 3hours(hrs) to process 6000 envelopes(e) --> equation 1, eq1
B+C took 2.5hrs to process the same no. of e i.e. 6000 --> eq2
A+C took 1hour(hr) to process 3000 e --> eq3
B took ?hr to process 12000 e --> this is the ask
From eq1,
A took, 3hr = 6000 e
so, in 1hr = ? e
Cross multiplying, A processed 2000 e in 1hr --> eq4
Substituting eq4 in eq3,
A+C took 1hr = 3000 e
A = 2000 e
so, C = 1000 e, in 1hr --> eq5
From eq2,
B+C took 2.5hr = 6000 e
so in 1hr = ? e
Cross multiplying, B+C processed 2400 e in 1hr --> eq6
From eq5,
C processed 1000 e in 1hr
Hence in eq6,
B+1000 = 2400
or B processed 1400 e in 1hr --> eq7
The ask is how many hours B took to process 12000 e
From eq7,
B took 1hr to process 1400 e.
1hr = 1400 e
?hr = 12000 e
Cross multiplying, it would take 12000/1400 = 60/7hrs to process 12000 e
A took 3hours(hrs) to process 6000 envelopes(e) --> equation 1, eq1
B+C took 2.5hrs to process the same no. of e i.e. 6000 --> eq2
A+C took 1hour(hr) to process 3000 e --> eq3
B took ?hr to process 12000 e --> this is the ask
From eq1,
A took, 3hr = 6000 e
so, in 1hr = ? e
Cross multiplying, A processed 2000 e in 1hr --> eq4
Substituting eq4 in eq3,
A+C took 1hr = 3000 e
A = 2000 e
so, C = 1000 e, in 1hr --> eq5
From eq2,
B+C took 2.5hr = 6000 e
so in 1hr = ? e
Cross multiplying, B+C processed 2400 e in 1hr --> eq6
From eq5,
C processed 1000 e in 1hr
Hence in eq6,
B+1000 = 2400
or B processed 1400 e in 1hr --> eq7
The ask is how many hours B took to process 12000 e
From eq7,
B took 1hr to process 1400 e.
1hr = 1400 e
?hr = 12000 e
Cross multiplying, it would take 12000/1400 = 60/7hrs to process 12000 e
17 Dec 2024, 06:01
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