What happens when two math instructors take a ski trip together?

What happens when two math instructors take a ski trip together? They make up math word problems as they travel.

 

I hope that you all enjoyed a restful President’s Day week, especially those who just took the February ACT (in case you missed it, multiple choice scores have begun to come out!).
 
My holiday was spent skiing in Killington, Vermont, where I joined forces with none other than John P of LogicPrep, who happened to also plan a trek up north for the weekend.

While you're on your way up north, here are a few possibly relevant math-y questions to keep your mind active (answers below!):

  1. We leave Armonk at 12:30 PM, destined for Killington, 240 miles away. Halfway to Killington, the car has averaged 60 miles per hour.  We'd like to arrive in Killington by 5:00 PM to pick up Ski/Snowboard equipment.  If we take a 30-minute pit stop right now, how fast do we need to drive, on average, the rest of the way, to arrive by 5:00 PM?  For a 60-minute stop? 
  2. Franky's Lift is due 3km west of the Express Lift, which takes you directly north 5km to Billy's Peak.  If Marcell's Trail is a straight shot path from Billy's to Franky's, approximately how many km long is it, to the nearest tenth?
  3. With a $100 budget for a group dinner, I can buy three orders of wings and three pizzas, tip $12, and have seven dollars left.  I can alternatively get five orders of wings with two pizzas and use the remaining money I have to provide a $13 tip.  How much does each order of wings and each pizza cost?  Assume that tax is included within each price.

Math aside, a good weekend in Killington should include a day or two on the slopes, equipment rental ideally secured off-site, a steak dinner at Wobbly Barn (though non-red meat options are certainly aplenty), and a brunch at Back Country Café.

Looking forward to seeing all of our students rejuvenated from the break!

-Matthew K, Instructor

 

Answers to questions above:
1. 30 min - 60mph, 60 min - 80 mph
2. 5.8 km
3. The (tax included) prices are $11 per order of wings and $16 per pizza