Simple Distance, Rate, Time Problem

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  • Thread starter MachineCode
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In summary, the book says that Helen travels faster than Anne, but when I put the equations together it says that Anne travels faster.
  • #1
MachineCode
4
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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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  • #2
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
 
  • #3
topsquark said:
Why do you think this is wrong?

-Dan
Because the book gives a different answer.
 
  • #4
MachineCode said:
Because the book gives a different answer.
I agree with your answers. Just to check, what are the book answers?

-Dan
 
  • #5
topsquark said:
I agree with your answers. Just to check, what are the book answers?

-Dan
The books answers are 60mph and 56mph
 
  • #6
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
 
  • #7
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.
 

FAQ: Simple Distance, Rate, Time Problem

What is the formula for solving a simple distance, rate, time problem?

The formula for solving a simple distance, rate, time problem is D = R x T, where D represents distance, R represents rate, and T represents time.

How do I know which units to use when solving a distance, rate, time problem?

The units used for distance, rate, and time should all be consistent. For example, if the distance is given in miles, the rate should be given in miles per hour and the time should be given in hours.

Can I use the same formula for all distance, rate, time problems?

Yes, the formula D = R x T can be used for all simple distance, rate, time problems. However, more complex problems may require additional formulas or equations.

How can I check my answer for a distance, rate, time problem?

You can check your answer by plugging your values back into the formula D = R x T and making sure the result is the same as the given distance. You can also use estimation or a different method to double check your answer.

What are some common mistakes to avoid when solving a distance, rate, time problem?

Some common mistakes to avoid include using inconsistent units, mixing up the order of the values (e.g. using rate as distance), and forgetting to convert units if necessary. It is also important to make sure you are using the correct formula for the specific problem.

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