The Ethnic food line at the Cougar Eat can serve customers at the rate of about 30 per hour. From 10 am until 4 pm one day, the rate R at which customers entered then line was about customers per hour at t hours past 10 am. About when was the waiting line the longest?
A)3:00 pm
B)2:45 pm
C)2:30 pm
D)2:15 pm

Question

The Ethnic food line at the Cougar Eat can serve customers at the rate of about 30 per hour. From 10 am until 4 pm one day, the rate R at which customers entered then line was about  customers per hour at t hours past 10 am. About when was the waiting line the longest?
A)3:00 pm 
B)2:45 pm 
C)2:30 pm 
D)2:15 pm

Quizplus · Accepted Answer

To find out when the waiting line was the longest, we need to calculate the difference between the rate at which customers entered the line and the rate at which the Ethnic food line can serve customers. This will give us the rate at which the line is growing.

At t hours past 10 am, the rate at which customers entered the line was:

R = 11eb69ff_fec0_feed_af94_751d58fa9bd5_TB8190_11 customers per hour

The rate at which the Ethnic food line can serve customers is:

S = 30 customers per hour

So, the rate at which the line is growing is:

G = R - S = 11eb69ff_fec0_feed_af94_751d58fa9bd5_TB8190_11 - 30 = -18eb69ff_fec0_feed_af94_751d58fa9bd5_TB8190_11 customers per hour

This means that the waiting line is getting shorter by 18eb69ff_fec0_feed_af94_751d58fa9bd5_TB8190_11 customers per hour. The longest waiting line will occur when the rate at which customers enter the line is at its maximum value, which is at t = 0, and the rate at which the Ethnic food line can serve customers is at its minimum value, which is 30 per hour.

Therefore, the longest waiting line will occur at 2:45 pm (4 hours and 45 minutes after 10 am).

The Ethnic Food Line at the Cougar Eat Can Serve