There are 450 boxes to load on a truck. A and B working independently

Question

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.

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Purnank · Answer

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.

tgsankar10 · Answer

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

Nidzo · Answer

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

HarishD · Answer

Answer D: Please see the image for explaination

There are 450 boxes to load on a truck. A and B working independently

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GMAT Data Sufficiency (DS) Questions

There are 450 boxes to load on a truck. A and B working independently

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