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If 5 people, each working at a constant rate can wash 8 cars

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by AbhishekRyu » Thu Oct 04, 2018 6:14 am

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If 5 people, each working at a constant rate can wash 8 cars in 40 mins, How many people working at a same constant rate are needed to wash a cars in b hours?

A) $$\frac{a\ }{60b}$$
B)$$\frac{5a}{12b}$$
C)$$\frac{a}{12b}$$
D)$$\frac{a}{20b}$$
E) $$\frac{25a}{b}$$
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If 5 people, each working at a constant rate can wash 8 cars

by regor60 » Thu Oct 04, 2018 8:38 am
AbhishekRyu wrote:If 5 people, each working at a constant rate can wash 8 cars in 40 mins, How many people working at a same constant rate are needed to wash a cars in b hours?

A) $$\frac{a\ }{60b}$$
B)$$\frac{5a}{12b}$$
C)$$\frac{a}{12b}$$
D)$$\frac{a}{20b}$$
E) $$\frac{25a}{b}$$
Since you know that 5, 8 and 40 minutes = 40/60 hours works, use this information to test the answers by using a=8 and b =40/60 =2/3 hours to see if any of the answers delivers the known answer of 5

A. a/60b = 8/(60*(2/3)) = 8/40 = 1/5 > not equal to 5

B. 5a/12b = (5x8)/(12x(2/3)) = 40/8 = 5 > equals 5 correct answer
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by [email protected] » Thu Oct 04, 2018 4:07 pm
Hi All,

We're told that 5 people, each working at a constant rate, can wash 8 cars in 40 MINUTES. We're asked how many people working at that same constant rate are needed to wash A cars in B HOURS. With these types of questions, it often helps to determine the total amount of work needed to complete a job.

Here, we have 5 people working for 40 minutes EACH. That's (5)(400) = 200 people-minutes of work needed to wash 8 cars.
By extension, it would take 200/8 = 25 people-minutes of work to wash 1 car.
Thus, to wash 1 car:
1 person would need 25 minutes
2 people would need 12.5 minutes each
3 people would need 8 1/3 minutes each
Etc.

We can use this work rate against the given question. Since 1 car wash requires 25 minutes of work, that's 25/60 = 5/12 hours for 1 person to wash 1 car. Thus, we're looking for an answer that equals 1 when A=1 and B=5/12. There's only one answer that matches....

Final Answer: B

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