Decisions, Decisions – Make One!

This is the second post of a series on decisions making.

If you didn’t read the first post, please check it out before continuing on.

In the first post, I ask you to respond to two questions. One was pretty straightforward, and the other was a bit more challenging. Did you get them right?

  • Together, a ball and a bat cost $1.10.  The bat costs one dollar more than the ball. How much does the ball cost?

Our minds like efficiency. We like to use our experience to develop the quick answer. We might consider it our intuition. For many people, this problem yields a quick answer that is also incorrect. The ball costs ten cents.  But if the total is one dollar and ten cents, then the bat must cost one dollar, making the bat only ninety cents more than the ball.  The correct answer is that the bat costs one dollar and five cents, and the ball costs five cents.

  • Hiking Harry likes two-day hikes. He camps out on a peak on the night between the two days. At 6am Saturday, Harry starts to hike up a modest 3,000 ft mountain. He stops along the way to rest, enjoy the views, take a few photos with his phone, and to just commune with nature. He arrives at the campsite at 6pm.  The next morning, he breaks camp and heads down the same trail, leaving at 6am. Again, he takes his time, but the downhill is generally easier. At 2pm he arrives at the trailhead where he began his journey the day before. Is there a place on this trail that Harry passes at exactly the same time of day on both days?  (Note that the problem is only asking you if there is a place, not asking you to solve for where that place might be.)

The reason so many people don’t like word problems – they are not efficient and frequently require more in-depth consideration. Did you answer “yes”?  You are correct if you did. But do you know for certain and can you provide some sort of proof of that answer? When I do this in training classes, people want to provide the “it depends” answer. But this is all about decisions and you need to make one. Yes or no?

The answer to this one is not too complicated. Imagine Harry has a clone that accurately replicates Harry’s day one ascent while the real Harry is coming down the path on day two. There is a point when Harry will come face to face with the clone. By definition, they will be in the same place at the same time. The answer is yes. Where and when I can’t predict, but I can say with certainty that there is a place and time where the two journeys intersect.

Our intuitions are more challenged by this problem. It’s not in our general experience, doesn’t have a simple mathematical solution (which problem number one does have, even though many of us don’t employ the simple algebra to find that answer), and we don’t know how to model it.

What’s your score so far? Are you two for two? If so, then you may have a good handle on your decision processes. Tomorrow, I’ll give you two decisions to make, and see how you do!

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