# Simple Distance, Rate, Time Problem

#### MachineCode

##### New member
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

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

##### Well-known member
MHB Math Helper
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

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

##### New member
Why do you think this is wrong?

-Dan
Because the book gives a different answer.

#### topsquark

##### Well-known member
MHB Math Helper
Because the book gives a different answer.

-Dan

#### MachineCode

##### New member

-Dan
The books answers are 60mph and 56mph

#### topsquark

##### Well-known member
MHB Math Helper
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

##### New member
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.