Amid the holiday grocery shopping madness, every line feels like the wrong one. And yet, some are wronger than others. Given equally capable cashiers, you are often better off bypassing the express lane. Research conducted at a large, unnamed, California grocery store found that while each item adds 3 seconds to the check-out time, it takes 41 seconds for a person to move through the line even before items are added to the tally. Bottom line: the big time-consumers are not the items, but the small talk and the paying. says Dan Meyer, who has a doctorate in math education from Stanford University:" (R224)

4 Amid the holiday grocery shopping madness, every line feels like the wrong one. And yet, some are wronger than others. Given equally capable cashiers, you are often better off bypassing the express lane. Research conducted at a large, unnamed, California grocery store found that while each item adds 3 seconds to the check-out time, it takes 41 seconds for a person to move through the line even before items are added to the tally. Bottom line: the big time-consumers are not the items, but the small talk and the paying. says Dan Meyer, who has a doctorate in math education from Stanford University:" (R224) Suppose you have 10 items in your cart, so you are allowed to use the express lane. How much longer must the line there be (compared to the regular lane) to make the wait in the regular lane less? You can answer that question with any strategy that makes sense to you, as long as you explain what you're thinking. If you need a starting place, one way is to use (a) Write the linear equations showing how the time it takes a shopper to check out depends on the number of items in her cart. (b) Suppose shoppers in the express lane buy 6 items (on average), while those in the regular lane buy about 20. Write the linear equations showing that your waiting time in each line depends on the number of shoppers ahead of you. (c) Now work on the main question - which line should you join when you have 10 items in your cart? How much longer must the express lane line be to make the wait on the regular lane line less? (Hint: The answer depends on the relative lengths of the lines, not the absolute difference in the lengths.)