Two runners start from the same point and run in the same direction. Runner A runs at 12 km/h, and Runner B runs at 10 km/h. If Runner B gets a 6-minute head start, after how many minutes from Runner A's start will Runner A catch up?

A. 25 min
B. 28 min
C. 30 min
D. 32 min

Question

High School

We appreciate your visit to Two runners start from the same point and run in the same direction Runner A runs at 12 km h and Runner B runs at. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

JessicaJessy JessicaJessy · Answer 1 · 2025-02-01T00:18:15-05:00

Let's solve the problem step-by-step involving the two runners, A and B.

Understand the question:
- Runner A runs at a speed of 12 km/h.
- Runner B runs at a speed of 10 km/h and has a 6-minute head start.

Convert head start time into hours:
[tex]\text{6 minutes} = \frac{6}{60} \text{ hours} = 0.1 \text{ hours}[/tex]

Determine the distance Runner B covers in the head start:
- In 0.1 hours, Runner B will cover:
  [tex]\text{Distance} = \text{Speed} \times \text{Time} = 10 \text{ km/h} \times 0.1 \text{ hours} = 1 \text{ km}[/tex]

Calculate when Runner A catches up to Runner B:
- Let [tex]t[/tex] be the time in hours after Runner A starts until they catch up.
- In [tex]t[/tex] hours, Runner A covers:
  [tex]12t[/tex]
- During the same [tex]t[/tex] hours, Runner B covers:
  [tex]10t + 1[/tex] (since Runner B initially had a 1 km lead)
- Set the distances equal since they meet at the same point:
  [tex]12t = 10t + 1[/tex]
- Solve for [tex]t[/tex]:
  [tex]12t - 10t = 1[/tex]
  [tex]2t = 1[/tex]
  [tex]t = 0.5[/tex] hours

Convert [tex]t[/tex] from hours to minutes:
- [tex]0.5[/tex] hours is [tex]0.5 \times 60 = 30[/tex] minutes

Therefore, Runner A will catch up with Runner B 30 minutes after Runner A starts. Hence, the correct multiple choice option is C. 30 min.