Two Passing Bicycles Word Problem

TL;DR

Two cyclists, Ann and Betty, start simultaneously and travel towards each other. They pass in 30 minutes, and it takes Ann 20 more minutes to reach the starting point of Betty. The question asks how many minutes after Ann arrives at point B will Betty reach point A.

Transcript

This is the last of the word problems that Kortaggio had sent, and they're all interesting because they're all involving distances and rates and times. They all involve you having to do a little bit of implicit algebra without having to explicitly solve for values of variables, and that's why they're fun. So this one says Ann and Betty, two cyclist... Read More

Key Insights

• ☠️ The problem involves calculating distances, rates, and times for two cyclists, Ann and Betty.
• 🐎 Ann and Betty start simultaneously and travel towards each other at constant speeds.
• 😥 Ann takes 30 minutes to reach the meeting point, and it takes her 20 additional minutes to reach Betty's starting point.
• 🗺️ The distance traveled by Ann is equal to 30 times her velocity, while the distance traveled by Betty is 45 times her velocity.

Questions & Answers

Q: How long does it take Ann to reach the point where she meets Betty?

Ann takes 30 minutes to reach the meeting point, which is the same distance as Betty's distance traveled.

Q: How long does it take Betty to reach point A after Ann arrives at point B?

Betty takes an additional 45 minutes to reach point A after Ann arrives at point B, totaling 25 minutes after Ann reaches point B.

Q: How is the distance traveled by Ann related to Betty's velocity?

The distance traveled by Ann is equal to 30 times Ann's velocity, and it is expressed as 45 times Betty's velocity.

Q: What is the relationship between Ann and Betty's velocities?

Ann's velocity is 3/2 times Betty's velocity, based on the distance they both travel.

Summary & Key Takeaways

• Ann and Betty start simultaneously and travel towards each other at constant speeds.

• They pass each other in 30 minutes.

• Ann takes an additional 20 minutes to reach Betty's starting point.