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Question 6
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Mr. Beecher and Mrs. Carter are teachers at the same school. They leave their houses at the same time in the morning to get to school.
Mr. Beecher frues 8 mikes away from school and rides his bicycle to work. Every minute, he gets of a mile closer to schoof.
Mrs. Carter lives 20 miles away from school and drives her car to work. Every minute, she gets of a mile closer to school.
After how many minutes will Mr. Beecher and Mrs. Carter first be the same distance away from school?
minutes

Ask by Fuentes Floyd. in the United States
Jan 24,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

After 36 minutes, Mr. Beecher and Mrs. Carter will be the same distance away from school.

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The Deep Dive

To find out when Mr. Beecher and Mrs. Carter will be the same distance away from school, let’s set up the equations based on their distances and the rates at which they’re traveling.
  1. Mr. Beecher’s distance from school after minutes:
  2. Mrs. Carter’s distance from school after minutes:
Now, we’ll set these two distances equal to each other to find :
Next, we solve for . First, we can eliminate the fractions by multiplying the entire equation by 6, the least common multiple of 6 and 2:
This simplifies to:
Next, we can rearrange the equation:
So, Mr. Beecher and Mrs. Carter will first be the same distance away from school after 36 minutes.

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