Crew A can build a car in 20 minutes and Crew B can build a car in 25 minutes. If both crews work independently and start at the same time, what is the least amount of time required for the two crews to build 10 complete cars?
A. 111 1/9 minutes B. 115 2/5 minutes C. 116 minutes D. 120 minutes E. 125 minutes
(D) In this problem, we cannot combine rates because the two crews are not working together. Each crew must build an integer number of cars. Instead, we will use logic to solve.
First, we know that Crew A will build at least 5 of the cars because it works faster. If both teams build 5 cars, Crew A will finish in 5 × 20 = 100 minutes and Crew B will finish in 5 × 25 = 125 minutes. In this scenario, it takes 125 minutes for the whole project to be complete.
If Crew A builds 6 of the cars, it will finish in 6 × 20 = 120 minutes. Crew B will have to build 4 cars and will finish in 4 × 25 = 100 minutes. So the project will be complete in only 120 minutes if Crew A builds 6 of the cars.
If Crew A builds any more than six of the cars, it will definitely take longer than 120 minutes since Crew A takes 20 minutes to build each car.
The correct answer is choice (D). ----------- Shouldn't the answer be A? This will be based if my below equation is correct: (x/20 + x/25) = 10
The both crews work INDEPENDENTLY. Therefore their rates CANNOT be combined and the equation you made is NOT correct in this case.
In other words the crews do NOT build any cars together. If the answer choice A had been correct, then the crew A would have built (1000/9) / 20 = 50/9 = 5 5/9 of a car. The crew B would have built (1000/9) / 25 = 40/9 = 4 4/9 of a car. In that case they would have built 9 complete cars, 5/9 of a one car and 4/9 of another car.
The answer is A not D. The question here is asking for the least amount of time required for the two crews to build 10 complete cars. Crew A will produce 6 cars in 120 mins. Crew B will produce 4.8 cars in 120 mins. (25 times 4 is NOT 100) The combined amount of time required here is 111 1/9 mins.
Dear student, you might have not paid enough attention to the word "independently" in the question statement. A lot of times just one word in the question statement can change the entire meaning and as the result the correct answer choice.
(25 times 4 is NOT 100)
In fact 25 × 4 = 100.
Crew A will produce 6 cars in 120 mins. Crew B will produce 4.8 cars in 120 mins.
So in 120 minutes crew A will produce 6 COMPLETE cars, while crew B will produce 4 COMPLETE cars (+ 1 UNCOMPLETED car). Therefore they will produce 10 COMPLETE cars in 120 minutes.
The combined amount of time required here is 111 1/9 mins.
How many COMPLETE cars will they produce in 111 1/9 minutes? Crew A will produce 5 COMPLETE cars (+ 1 uncompleted) Crew B will produce 4 COMPLETE cars (+ 1 uncompleted) So in 111 1/9 minutes they will produce only 9 COMPLETE cars, while the question statement requires 10 complete cars to be produced.
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