Question

Part I: Making the Race

Henri is Emile's younger brother and they are having a walking race. Emile can walk 2.5 meters per second whereas Henri walks 1 meter per second. Because Emile is faster, they give Henri a 45 meter head start. Emile knows Henri would enjoy winning the race, but they do not want to make the race so short that it is obvious Emile let Henri win.


1. How long should the race be so that Henri will win in a close race?

2. Describe or show your strategy on how you came up with your answer for #1.

Answer 1

Explanation:

To make the race close, the length of the race should be 450 meters.

Here's the reasoning behind the answer:

Let's first calculate how long it would take for Emile to catch up to Henri, assuming Henri starts 45 meters ahead.

The time it takes Emile to cover the same 45-meter distance is 45/2.5 = 18 seconds.

During this time, Henri would have walked a distance of 1 x 18 = 18 meters.

So, after 18 seconds, Emile will have caught up to Henri and will be 27 meters ahead of him (45 - 18 = 27).

To make the race close, we want Henri to finish just a split second before Emile. So, we can assume that Henri will finish the race just as Emile catches up to him.

Let's call the total distance of the race "d."

So, Henri will walk d meters, while Emile will walk d + 27 meters (the 27 meters is the distance Emile has to walk after catching up to Henri).

We can set up an equation to solve for d:

d/1 = (d + 27)/2.5

Solving for d, we get:

d = 450

So, the race should be 450 meters long for Henri to win in a close race.