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There are 450 boxes to load on a truck. A and B working independently but at the same time take 30 minutes to load the truck. How long should it take B working by himself to load the truck?
(1) A loads twice as many boxes as B
(2) A would take 45 minutes by himself.
_________________
(1) A loads twice as many boxes as B
(2) A would take 45 minutes by himself.
_________________
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I think D,
There are 450 boxes to load on a truck. A and B working independently but at the same time take 30 minutes to load the truck.
Assuming their efficiency to load truck A boxes/min and B boxes/min,
Therefore, 30*(A+B) = 450
A+B = 15--Eq1
How long should it take B working by himself to load the truck?
1st - A loads twice as many boxes as B
A=2B Substituting in eq1 3B = 15
B=5
Time taken by B load truck = 450 / 5 = 90mins Sufficient.
2nd - A would take 45 minutes by himself.
A efficiency = 450 / 45 = 10
Therfore B = 5 from eq1
Time taken by B load truck = 450 / 5 = 90mins Sufficient.
There are 450 boxes to load on a truck. A and B working independently but at the same time take 30 minutes to load the truck.
Assuming their efficiency to load truck A boxes/min and B boxes/min,
Therefore, 30*(A+B) = 450
A+B = 15--Eq1
How long should it take B working by himself to load the truck?
1st - A loads twice as many boxes as B
A=2B Substituting in eq1 3B = 15
B=5
Time taken by B load truck = 450 / 5 = 90mins Sufficient.
2nd - A would take 45 minutes by himself.
A efficiency = 450 / 45 = 10
Therfore B = 5 from eq1
Time taken by B load truck = 450 / 5 = 90mins Sufficient.
Posts: 281
Combined rate to load 450 boxes is 30 minutes
\(\frac{1}{A} + \frac{1}{B} = \frac{1}{30}\)
Rate of B?
Statement 1: A loads twice as many boxes as B
Rate of A is half as rate of B
\(\frac{1}{A} = \frac{2}{B}\)
\(\frac{2}{B} + \frac{1}{B} = \frac{1}{30}\)
SUFFICIENT
Statement 2: A would take 45 minutes by himself
Rate of A is \(\frac{1}{45}\)
\(\frac{1}{45} + \frac{1}{B} = \frac{1}{30}\)
SUFFICIENT
Answer is D
\(\frac{1}{A} + \frac{1}{B} = \frac{1}{30}\)
Rate of B?
Statement 1: A loads twice as many boxes as B
Rate of A is half as rate of B
\(\frac{1}{A} = \frac{2}{B}\)
\(\frac{2}{B} + \frac{1}{B} = \frac{1}{30}\)
SUFFICIENT
Statement 2: A would take 45 minutes by himself
Rate of A is \(\frac{1}{45}\)
\(\frac{1}{45} + \frac{1}{B} = \frac{1}{30}\)
SUFFICIENT
Answer is D
Let the time it takes A = \(a\) and the time is takes B = \(b\)
We are told that working together it takes them 30 minutes, or 0.5 hours: \(\frac{1}{a}+\frac{1}{b} = \frac{1}{0.5}\)
\(\frac{a+b}{ab}= \frac{1}{0.5}\)
\(a+b = 2ab\)
If we either know the ratio of a to b, or know the value of a, then we will have enough to be able to solve the question.
(1) A loads twice as many boxes as B
As A loads twice as many boxes as B, then we know \(a = 0.5b\)
SUFFICIENT
SOLVING:
Plugging in \(a = 0.5b\) into \(a+b = 2ab\):
\((0.5)b+b = 2(0.5b)b\)
\(1.5b = b^2\)
\(b = 1.5\) hours
(2) A would take 45 minutes by himself
45 minutes is \(\frac{3}{4}\) of an hour. \(a = \frac{3}{4}\)
SUFFICIENT
SOLVING:
Plugging in \(a = \frac{3}{4}\) into \(a+b = 2ab\):
\(\frac{3}{4}+b = 2(\frac{3}{4})b\)
\(\frac{3}{4} = \frac{1}{2}b\)
\(b = \frac{3}{2} = 1.5\) hours
ANSWER D
We are told that working together it takes them 30 minutes, or 0.5 hours: \(\frac{1}{a}+\frac{1}{b} = \frac{1}{0.5}\)
\(\frac{a+b}{ab}= \frac{1}{0.5}\)
\(a+b = 2ab\)
If we either know the ratio of a to b, or know the value of a, then we will have enough to be able to solve the question.
(1) A loads twice as many boxes as B
As A loads twice as many boxes as B, then we know \(a = 0.5b\)
SUFFICIENT
SOLVING:
Plugging in \(a = 0.5b\) into \(a+b = 2ab\):
\((0.5)b+b = 2(0.5b)b\)
\(1.5b = b^2\)
\(b = 1.5\) hours
(2) A would take 45 minutes by himself
45 minutes is \(\frac{3}{4}\) of an hour. \(a = \frac{3}{4}\)
SUFFICIENT
SOLVING:
Plugging in \(a = \frac{3}{4}\) into \(a+b = 2ab\):
\(\frac{3}{4}+b = 2(\frac{3}{4})b\)
\(\frac{3}{4} = \frac{1}{2}b\)
\(b = \frac{3}{2} = 1.5\) hours
ANSWER D
Answer D: Please see the image for explaination
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