Simple Distance, Rate, Time Problem

[MachineCode]

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

 

[topsquark]

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

 

[MachineCode]

Why do you think this is wrong?

-Dan

Because the book gives a different answer.

 

[topsquark]

Because the book gives a different answer.

I agree with your answers. Just to check, what are the book answers?

-Dan

 

[MachineCode]

I agree with your answers. Just to check, what are the book answers?

-Dan

The books answers are 60mph and 56mph

 

[topsquark]

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

 

[MachineCode]

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.