Crew A can build a complete car in 20 minutes and Crew B can build

Question

Crew A can build a complete car in 20 minutes and Crew B can build a complete car in 25 minutes. If both crews work independently and start at the same time, what is the shortest amount of time it could take for 10 cars to be complete?

A. 111 1/9 minutes
B. 115 2/5 minutes
C. 116 minutes
D. 120 minutes
E. 125 minutes

A. 111 1/9 minutes
B. 115 2/5 minutes
C. 116 minutes
D. 120 minutes
E. 125 minutes

PyjamaScientist · Answer

New Correct solution:  
 
Well this one got me too, and this is why I am keeping the original answer posted. I also missed the part of A and B working independently  not together.  But, since they are not working together, my above solution is wrong.

Solution to the problem when both A and B are working independently is much easier, with almost no calculation required.
It's given that A can build a car in 20 mins, and B can build a car in 25 mins. So, Work rate of A is > that of B. So, if they work for similar no. of hours, A would make more than B does. Since, the #no. of cars is going to be an " integer ", we have to take the no. of minutes as the LCM of the (20, 25). That is 100 mins. So, for 100 mins, A would produce 5 cars ( \frac{100}{20}=5 ), and B would produce 4 cars ( \frac{100}{25}=4 ). So, that is 9 cars. Now the question asks us the time required to make 10 cars. Since, we have 9 out of 10 cars already, one car left would be made by A in lesser time than B. So, in another 20 minutes we will have one more car made by A. So, the total time taken to get 10 cars when both A and B are working independently is 100 + 20 mins =  120 mins .   Option (D).

Kalli1 · Answer

Those two crews work independently so ,
 In the first 100 minutes , the first crew with ratio 1/20 is going to complete 5 cars.
In the first 100 minutes , the second crew with ratio 1/25 is going to complete 4 cars.
So it misses 1 car. The first crew is going complete it faster than second 100 + 20=120 minutes. 
 Correct D

colfer · Answer

Both crews are working independently . When crew A finishes 5 cars crew B will finish 4 cars. Total of 9 cars. 10th car will be done by the quicker crew A in another 20 min. Total of 120min

Posted from my mobile device

adityaprateek15 · Answer

Since the time taken to produce a car by Crew A and B are in ratio 4:5, ratio of their rates will be 5:4 which means for every 5 car A makes, B will make 4. Since, A is faster, A will make 5 cars in 100 mins and B will make 4 in that same amount of time.

Now, one more car would take less time if A makes it. Hence, 100+20 = 120 (Option D)

Crew A can build a complete car in 20 minutes and Crew B can build

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Crew A can build a complete car in 20 minutes and Crew B can build

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