If shoppers enter a store at an average rate of $r$ shoppers per minute and each stays in the store for average time of $T$ minutes, the average number of shoppers in the store, $N$, at any one time is given by the formula $N=rT$. 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 of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.
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 many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?
Please someone help me find an answer to this question. My steps:
$$ \frac{84}{5} = 16.8 $$ $$ N = rt \Rightarrow (16.8)(5) $$ $$ N = 84 $$
For me answer was coming 84 but the answer given was 7.
You need to make sure that all the variables use the same unit of time.
If 84 shoppers make a purchase per hour, then you have $ \frac{84}{60} = 1.4 $ shoppers making a purchase per minute, so you have $r = 1.4$ and $t = 5$. Then, plugging into Little's law, you have $ N = 1.4*5 = 7$.
Alternatively, you could transform $t = 5 \ \text{min} \rightarrow t = \frac{1}{12} \ \text{hour} $, in which case you'd have $ N = 84*\frac{1}{12} = 7$.