Simple Distance, Rate, Time Problem

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SUMMARY

The discussion revolves around a distance, rate, and time problem involving two sisters, Helen and Anne, who live 332 miles apart. Helen drove for 3.2 hours at a speed that is 4 mph faster than Anne, who drove for 2.8 hours. The derived equation, 2.8r + 3.2(r+4) = 332, led to incorrect speeds of 57.2 mph for Helen and 53.2 mph for Anne, while the book states the correct speeds are 60 mph for Helen and 56 mph for Anne. The discrepancy suggests that the book's answers may be incorrect, as the calculated distances exceed the total distance of 332 miles.

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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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