# Major problem- finding the distance between two cities

1. Feb 15, 2007

### intelx86

1. The problem statement, all variables and given/known data
Cyclist rode from one city to another city. First day he rode 1/6th from all the distance and plus 50 km. On second day he rode 1/5th from all the road plus 15 km. And on the third day he rode 1/20 from all distance plus 70km. And the question is how long was the distance between two cities.

2. Relevant equations
I have no idea where to begin . I think the distance should be x. But what comes next? Sorry for my bad English, as it is not my native language.

3. The attempt at a solution

I thought it should look like 1/6*x +50 + 1/5*x +15 +1/20 +70 = ???
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 15, 2007

### cristo

Staff Emeritus
Well, the left hand side of this equation is the total distance he covers. Supposing that he reaches the city, then what will this be equal to? (i.e. what is x?)

3. Feb 15, 2007

### intelx86

Well the x is the distance he covers. Maybe it should be equal to 3 (as he rode it three days). Frankly I have no clue.
But I am curious was the equation I wrote even the right one?

Last edited: Feb 15, 2007
4. Feb 15, 2007

### cristo

Staff Emeritus
Correct, x denotes the total distance he covers.

On the left hand side of that equation you have the sum of the distances he covers on the three days, i.e. the total distance he covers.

Now is it clearer?

Yes

5. Feb 15, 2007

### intelx86

1/6*x +50 + 1/5*x +15 +1/20 *x +70 =x
Should it be like that?
And then:
-7/12 *x= -135
And then result should be like x= 231 3/7 ?
It sounds strange in my opinion.

Last edited: Feb 15, 2007
6. Feb 15, 2007

### cristo

Staff Emeritus
That's correct. Why do you think it sounds strange?

7. Feb 15, 2007

### intelx86

I do not know, maybe the fraction as a result sounds not so nice.
But if you say it is right, then well. I will have to give my homework in for tomorrow, so Ill see and will post a comment if I get it back.
So you think its the right solution?

8. Feb 15, 2007

### cristo

Staff Emeritus
Yes, it is the correct solution.