Yoak: A Rather Odd Car Trip
Here’s a puzzle that sounds a little like those, “A train leaves…” questions we were all prepared for but rarely saw on the SAT, but with a twist.
You are going to take a drive from City A to City B and back, but in a rather unusual car. When travelling uphill, the car always moves at exactly 56 miles per hour. On level ground, it travels at 63 miles per hour and finally when travelling downhill it travels at 72 miles per hour. Assume that it transitions from one speed to another instantaneously and all of those other “mathematically perfect” qualities that make questions like this answerable.
You find that travelling from City A to City B takes exactly 4 hours of travel time. On the return trip, driving time sums to 4 hours and 40 minutes.
How far apart are Cities A and B?
The Math Factor in iTunes
RSS feed
Comments RSS
mathbun.com
czarandy said,
April 20, 2009 at 8:02 pm
Show Spoiler ▼
jyoak said,
April 21, 2009 at 9:10 am
czarandy, about your solution…
Show Spoiler ▼
nklein said,
April 21, 2009 at 11:29 am
That was a fun problem. I spent most of it grudgingly going through the motions expecting to find a range of answers. Alas, they collapsed nicely in the end. Bonus.
pjrogers said,
April 21, 2009 at 3:50 pm
Show Spoiler ▼
Fun!
jyoak said,
May 4, 2009 at 3:26 pm
I’ve posted some more of my own thoughts as a followup in a later post here: http://mathfactor.uark.edu/2009/05/04/yoak-followup-to-a-rather-odd-car-trip/ .