Calculate the distance Odalis is from the checkpoint when catching up to Jaquan given their different speeds and start times | Step-by-Step Solution

Hi there! This is a classic "catch-up" problem that combines distance, speed, and time.

What We're Solving:

We need to find how far from the checkpoint both Jaquan and Odalis will be when Odalis catches up to Jaquan, given that Jaquan has a 2-minute head start but runs slower.

The Approach:

The key insight is that when Odalis "catches up," both runners will be at the same distance from the checkpoint. We'll use the relationship: Distance = Speed × Time. Since Jaquan gets a head start, we need to account for that extra time he's been running.

Step-by-Step Solution:

Step 1: Set up our variables

• Let t = time (in hours) that Odalis has been running when they meet
• Jaquan runs for (t + 2/60) hours total, since he had a 2-minute = 2/60 hour head start

Step 2: Write distance equations for both runners

• Jaquan's distance from checkpoint = 9 × (t + 2/60) km
• Odalis's distance from checkpoint = 12 × t km

Step 3: Set up the equation When they meet, their distances from the checkpoint are equal: 9(t + 2/60) = 12t

Step 4: Solve for t 9t + 9(2/60) = 12t 9t + 18/60 = 12t 9t + 0.3 = 12t 0.3 = 12t - 9t 0.3 = 3t t = 0.1 hours

Step 5: Find the distance Odalis's distance = 12 × 0.1 = 1.2 km (We can verify: Jaquan's distance = 9 × (0.1 + 2/60) = 9 × 0.133... = 1.2 km ✓)

The Answer:

Odalis will be 1.2 km past the checkpoint when they catch up to Jaquan.

Memory Tip:

Think of it like this: "The faster runner needs time to make up for the slower runner's head start." Set their distances equal at the meeting point, and solve for when that happens!

Great job working through this challenging problem! The trickiest part is remembering to convert minutes to hours and accounting for the head start time. You've got this! 🌟