Simple Distance, Rate, Time Problem

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Discussion Overview

The discussion revolves around a distance, rate, and time problem involving two sisters, Helen and Anne, who travel to meet each other. Participants are attempting to solve for their average speeds based on the given conditions and comparing their results to a book answer.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Participants derive the equation 2.8r + 3.2(r+4) = 332 to solve for the average speeds of Helen and Anne.
  • One participant calculates Anne's speed as 53.2 mph and Helen's speed as 57.2 mph, based on their derived equation.
  • Another participant notes that the book provides different answers: Helen at 60 mph and Anne at 56 mph.
  • Concerns are raised that if the book's answers are correct, the total distance traveled would exceed 332 miles, suggesting a potential error in the book.
  • Participants express uncertainty about the correctness of their calculations and the book's answers, with one participant stating they have reviewed their work multiple times.

Areas of Agreement / Disagreement

There is no consensus on the correctness of the book's answers versus the participants' calculations. Some participants agree with the calculated speeds, while others question the validity of the book's answers.

Contextual Notes

Participants have not resolved the discrepancies between their calculations and the book's answers, and there are unresolved assumptions regarding the accuracy of the derived equation.

MachineCode
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Not sure what I'm doing wrong...

Problem:

Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister’s house partway between
their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen’s average speed was four miles per hour faster than
Anne’s. Find Helen’s average speed and Anne’s average speed.

Book Answer: Helen = 60mph, Anne = 56 mph

My work:

// This is the equation I derived
2.8r + 3.2(r+4) = 332

// Solve
= 2.8r + 3.2r + 12.8 = 332
= (2.8r + 3.2r) + 12.8 = 332
= 6.r + 12.8 = 332
= 6r = (332-12.8)
= (6r/6r) = (319.2/6r)
r = 53.2

Helen = 53.2 + 4

My Answer:

Helen: 57.2 mph, Anne: 53.2mph

Check:

57.2 x 3.2 = 183.04
53.2 x 2.8 = 148.96

183.04 + 148.96 = 332
 
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MachineCode said:
Not sure what I'm doing wrong...

Problem:

Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister’s house partway between
their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen’s average speed was four miles per hour faster than
Anne’s. Find Helen’s average speed and Anne’s average speed.

Book Answer: Helen = 60mph, Anne = 56 mph

My work:

// This is the equation I derived
2.8r + 3.2(r+4) = 332

// Solve
= 2.8r + 3.2r + 12.8 = 332
= (2.8r + 3.2r) + 12.8 = 332
= 6.r + 12.8 = 332
= 6r = (332-12.8)
= (6r/6r) = (319.2/6r)
r = 53.2

Helen = 53.2 + 4

My Answer:

Helen: 57.2 mph, Anne: 53.2mph

Check:

57.2 x 3.2 = 183.04
53.2 x 2.8 = 148.96

183.04 + 148.96 = 332
Why do you think this is wrong?

-Dan
 
topsquark said:
Why do you think this is wrong?

-Dan
Because the book gives a different answer.
 
MachineCode said:
Because the book gives a different answer.
I agree with your answers. Just to check, what are the book answers?

-Dan
 
topsquark said:
I agree with your answers. Just to check, what are the book answers?

-Dan
The books answers are 60mph and 56mph
 
MachineCode said:
The books answers are 60mph and 56mph
That would mean that the combined distance traveled is greater than 332 mi. (You can check this yourself.) The book is wrong.

-Dan
 
topsquark said:
That would mean that the combined distance traveled is greater than 332 mi. (You can check this yourself.) The book is wrong.

-Dan
I really think that is the case, I've gone over this over and over again. Thanks For you help.
 

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