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Simple Distance, Rate, Time Problem

MachineCode

New member
Feb 2, 2020
4
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

Well-known member
MHB Math Helper
Aug 30, 2012
1,356
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

New member
Feb 2, 2020
4

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,356

MachineCode

New member
Feb 2, 2020
4

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,356
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
Feb 2, 2020
4
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.