Do We Have Time to Make It Back for the Party? (A Desmos Experiment)

The Question

As I walked out of the March SAT, I found my parents sitting anxiously in the car. We were leaving for Spring Break in South Carolina and had a long drive ahead of us. About four hours in, though, my girlfriend texted that her flight had been canceled and she was now able to attend our friend’s birthday party. Could I come?

This felt like a simple question—but it turned into a math problem pretty quickly.

The Situation

We were about X miles away, and the party started at 7:30 PM.

I started thinking:

• How fast are we actually going (not just speed limit)?

• How much time will we lose stopping?

• What time would we realistically arrive?

Instead of guessing, I decided to model it.

The Experiment (Using Desmos)

I opened Desmos Graphing Calculator and set up a simple model.

Step 1: Time = Distance / Speed

I started with:

time = distance ÷ speed

But then I adjusted it to be more realistic:

average speed ≠ highway speed

added buffer time for stops

So the model became something like:

total time = (distance ÷ avg speed) + stop time

Step 2: Build It Visually

In Desmos, I created a graph where:

x = time

y = distance remaining

Then I could visually see:

how long the trip would take

what arrival time that meant

Step 3: Test Scenarios

This was the fun part.

I tested:

What if we average 65 mph?

What if traffic slows us to 55 mph?

What if we stop once vs twice?

Each change gave a slightly different arrival time.

What I Found

At first, I thought we’d easily make it. But once I added realistic assumptions:

• lower average speed

• time for stops

• slight delays

• my parents real reluctance

…it became clear. We could do it and wouldn’t even be that late!

What Actually Happened

We kept going. Argh. So sadly I didn’t get to compare the results to what the model predicted.

What I Learned

This was a simple problem, but it changed how I think about decisions. Instead of guessing: “Yeah, we’ll probably make it…” I started thinking: “What assumptions am I making—and can I test them?”