SAT Mathematics Practice Test 3

Questions 57 and 58 refer to the following information.

If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for an average time of

T

minutes, the average number of shoppers in the store,

N

, at any one time is given by the formula

N r=T

. This relationship is known as Little’s law.
The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of15 minutes. The store owner uses Little’s law to estimate that there are 45 shoppers in the store at any time.

Question : 57 of 58

Marks: +1, -0

Little’s law can be applied to any part of the store,such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how manyshoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?

Your Answer:

Validate

Solution:

The average number of shoppers, N, in the check outline at any time is N = rt,
where r is the number of shoppers entering the checkout line per minute and T is the average number of minutes each shopper spends in the checkout line.
Since 84 shoppers per hour make a purchase, 84 shoppers per hour enter the checkout line.
This needs to be converted to the number of shoppers per minute.
Since there are 60 minutes in one hour, the rate is

{84 \text "shoppers"}/{60 \text "minutes"}

1.4 shoppers per minute.
Using the given formula with r = 1.4 and t = 5 yields N = rt = (1.4)(5) = 7.
Therefore, the average number of shoppers, N, in the checkout line at any time during business hours is 7.

Go to Question:

Prev Question

Next Question