# Major problem- finding the distance between two cities

## Homework Statement

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.

## Homework 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.

## The Attempt at a Solution

I thought it should look like 1/6*x +50 + 1/5*x +15 +1/20 +70 = ???

cristo
Staff Emeritus

## Homework Statement

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.

## Homework 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.

## The Attempt at a Solution

I thought it should look like 1/6*x +50 + 1/5*x +15 +1/20 +70 = ???
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?)

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:
cristo
Staff Emeritus
Well the x is the distance he covers.

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?

But I am curious was the equation I wrote even the right one?
Yes

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:
cristo
Staff Emeritus
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.

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

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?

cristo
Staff Emeritus