# Rate distance Time Problem

#### Ebba Sen Pai

##### New member
I cannot for the life in me discover what I am doing wrong with this question. I know there are different formats and methods for finding the solution, but using the only one taught in my book I seem to be fundamentally misunderstanding something. If anyone can tell me the error of my ways I would be humbled beyond measure.

Question:
A man walks at the rate of 4 miles per hour. How far can he walk into the country and ride back on a trolley that travels at the rate of 20 miles per hour, if he must be back home 3 hours from the time he started?

My Solving Attempt:

Rate\/ Time \/ Distance \/
__________________________
Walk | 4 | 3-t | 12-4t | (I find distance by multiplying rate x time)
Trolley | 20 | t | 20t |
------------------------------
(I write as algebraic formula)

12-4t=20t (I add 4 to both sides)
12=24t (I divide both sides by 24)
0.5=t

My book says the correct answer is 10
Where have I gone so wrong?

#### Subhotosh Khan

##### Super Moderator
Staff member
I cannot for the life in me discover what I am doing wrong with this question. I know there are different formats and methods for finding the solution, but using the only one taught in my book I seem to be fundamentally misunderstanding something. If anyone can tell me the error of my ways I would be humbled beyond measure.

Question:
A man walks at the rate of 4 miles per hour. How far can he walk into the country and ride back on a trolley that travels at the rate of 20 miles per hour, if he must be back home 3 hours from the time he started?

My Solving Attempt:

Rate\/ Time \/ Distance \/
__________________________
Walk | 4 | 3-t | 12-4t | (I find distance by multiplying rate x time)
Trolley | 20 | t | 20t |
------------------------------
(I write as algebraic formula)

12-4t=20t (I add 4 to both sides)
12=24t (I divide both sides by 24)
0.5=t

My book says the correct answer is 10
Where have I gone so wrong?
The FIND of the problem is " How far can he walk ". So let us assume that he walked the distance d miles

He took (d/4) hours to walk.

The trolley took (d/20) hours to come back.

Hence:

d/4 + d/20 = 3

Now solve for 'd'.

#### Dr.Peterson

##### Elite Member
I cannot for the life in me discover what I am doing wrong with this question. I know there are different formats and methods for finding the solution, but using the only one taught in my book I seem to be fundamentally misunderstanding something. If anyone can tell me the error of my ways I would be humbled beyond measure.

Question:
A man walks at the rate of 4 miles per hour. How far can he walk into the country and ride back on a trolley that travels at the rate of 20 miles per hour, if he must be back home 3 hours from the time he started?

My Solving Attempt:

Rate\/ Time \/ Distance \/
__________________________
Walk | 4 | 3-t | 12-4t | (I find distance by multiplying rate x time)
Trolley | 20 | t | 20t |
------------------------------
(I write as algebraic formula)

12-4t=20t (I add 4 to both sides)
12=24t (I divide both sides by 24)
0.5=t

My book says the correct answer is 10
Where have I gone so wrong?
There are several ways to do this. You chose to define a variable as the time spent on the trolley, so you are not directly finding what was asked for. The question is, how far he walks (which is the same as the distance on the trolley). So, how far is that? 20t = 20(0.5) = 10. That is the answer!

When you start a problem like this, it is a good habit to write down what the variable means; then when you finish, you will be reminded that your 0.5 is the time. Then you check what is being asked, and use the result from the equation to answer it, as I did above. Solving the equation is not the end of the problem!

Bottom line: You did a great job writing and solving the equation. Just don't stop thinking after doing the math.

#### Jomo

##### Elite Member
I cannot for the life in me discover what I am doing wrong with this question. I know there are different formats and methods for finding the solution, but using the only one taught in my book I seem to be fundamentally misunderstanding something. If anyone can tell me the error of my ways I would be humbled beyond measure.

Question:
A man walks at the rate of 4 miles per hour. How far can he walk into the country and ride back on a trolley that travels at the rate of 20 miles per hour, if he must be back home 3 hours from the time he started?

My Solving Attempt:

Rate\/ Time \/ Distance \/
__________________________
Walk | 4 | 3-t | 12-4t | (I find distance by multiplying rate x time)
Trolley | 20 | t | 20t |
------------------------------
(I write as algebraic formula)

12-4t=20t (I add 4 to both sides)
12=24t (I divide both sides by 24)
0.5=t

My book says the correct answer is 10
Where have I gone so wrong?
You did not do anything wrong other than finishing the problem. I am sure that you know that your variable t stood for time. But the question ask for the distance. The distance is d =12-4t or 20t (they are equal to one another) and you know t = .5. So now find d!
I hope that the book does not say that the answer is 10, as that is wrong. The answer is 10 miles.
BTW, great work up to here.

#### Ebba Sen Pai

##### New member
There are several ways to do this. You chose to define a variable as the time spent on the trolley, so you are not directly finding what was asked for. The question is, how far he walks (which is the same as the distance on the trolley). So, how far is that? 20t = 20(0.5) = 10. That is the answer!

When you start a problem like this, it is a good habit to write down what the variable means; then when you finish, you will be reminded that your 0.5 is the time. Then you check what is being asked, and use the result from the equation to answer it, as I did above. Solving the equation is not the end of the problem!

Bottom line: You did a great job writing and solving the equation. Just don't stop thinking after doing the math.
Thank you ! That really helped!

#### Ebba Sen Pai

##### New member
You did not do anything wrong other than finishing the problem. I am sure that you know that your variable t stood for time. But the question ask for the distance. The distance is d =12-4t or 20t (they are equal to one another) and you know t = .5. So now find d!
I hope that the book does not say that the answer is 10, as that is wrong. The answer is 10 miles.
BTW, great work up to here.
Thank you so much! I can "see" exactly how to do this type of question now.

#### Ebba Sen Pai

##### New member
There are several ways to do this. You chose to define a variable as the time spent on the trolley, so you are not directly finding what was asked for. The question is, how far he walks (which is the same as the distance on the trolley). So, how far is that? 20t = 20(0.5) = 10. That is the answer!

When you start a problem like this, it is a good habit to write down what the variable means; then when you finish, you will be reminded that your 0.5 is the time. Then you check what is being asked, and use the result from the equation to answer it, as I did above. Solving the equation is not the end of the problem!

Bottom line: You did a great job writing and solving the equation. Just don't stop thinking after doing the math.
Thank you so much! This makes perfect sense now!   