Total travelled distance of a man

[DaexmaretGigis]

A man was moving at an avg speed of 30 km/h. When he had 40km less left to pass than what he had already travelled, he reduced the speed to 20 km/h and the avg speed of the whole trip became 25 km/h. How much has the man travelled so far?

My guess was to get the speed for the first part of the trip. I named the first part of the trip X and the second X-40. To calculate total travelled distance, I tried adding the X and X-40 and then converting the speed into the v1t1+v2t2 formula, but I do not know how much time they had travelled. I again tried to calculate the movement speed on the first part of the trip, but that really doesn't help me. How do I solve this problem?

 

[Deleted member 4993]

A man was moving at an avg speed of 30 km/h. When he had 40km less left to pass than what he had already travelled, he reduced the speed to 20 km/h and the avg speed of the whole trip became 25 km/h. How much has the man travelled so far?

My guess was to get the speed for the first part of the trip. I named the first part of the trip X and the second X-40. To calculate total travelled distance, I tried adding the X and X-40 and then converting the speed into the v1t1+v2t2 formula, but I do not know how much time they had travelled. I again tried to calculate the movement speed on the first part of the trip, but that really doesn't help me. How do I solve this problem?

This problem, as written does not make sense to me. It asks at the end:

How much has the man travelled so far?​

How far from where - how far to where?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[lev888]

I would use the average speed formula to set up the equation. Write down the formula, then substitute everything with expressions that use the givens and your variable.

 

[DaexmaretGigis]

I would use the average speed formula to set up the equation. Write down the formula, then substitute everything with expressions that use the givens and your variable.

If the avg speed formula is total distance travelled / total time and we don't know the time, do I substitute it with the total time formula? Total distance/speed? In that case, I use the latest avg speed value, right?

 

[DaexmaretGigis]

This problem, as written does not make sense to me. It asks at the end:

How much has the man travelled so far?​

How far from where - how far to where?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

I'm not sure which part I forgot to explain, though. The question is basically what distance did the man cover from start to finish. I named the first part of the trip X, the second X-40, don't know the time and that stops me from calculating. Didn't I mention that in the post? :/

 

[lev888]

If the avg speed formula is total distance travelled / total time and we don't know the time, do I substitute it with the total time formula? Total distance/speed? In that case, I use the latest avg speed value, right?

Total time is the sum of 2 times. Each one can be expressed using the givens and the variable.

 

[Steven G]

You named the 1st part of the trip X. So X is just the name of the trip! X does not represent distance, X does not represent time and X does not represent speed. Is that really what you wanted? I think not. You wanted to say that X represented the DISTANCE travelled for the 1st part of the trip. Is that clear?

Let X = the distanced travelled in the 1st part of the trip.
Let X-40 = the distanced travelled in the 2nd part of the trip.

For the 1st part of the trip, the average speed was 30 km/hr.
The average speed for the 2nd part of the trip was 20 km/hr.

The average speed for the entire trip is 25 km/hr.
How far, in terms of X, was the entire trip?

Can you finish up? Do you have enough information?

 

[Steven G]

A man was moving at an avg speed of 30 km/h. When he had 40km less left to pass than what he had already travelled, he reduced the speed to 20 km/h and the avg speed of the whole trip became 25 km/h. How much has the man travelled so far?

My guess was to get the speed for the first part of the trip.

The speed for the 1st part of the trip was 30 km/hr. What did you think the 30 km/hr stand for? Did it stand for the 2nd part of the trip? Is it the average speed for the whole trip?

 

[DaexmaretGigis]

You named the 1st part of the trip X. So X is just the name of the trip! X does not represent distance, X does not represent time and X does not represent speed. Is that really what you wanted? I think not. You wanted to say that X represented the DISTANCE travelled for the 1st part of the trip. Is that clear?

Let X = the distanced travelled in the 1st part of the trip.
Let X-40 = the distanced travelled in the 2nd part of the trip.

For the 1st part of the trip, the average speed was 30 km/hr.
The average speed for the 2nd part of the trip was 20 km/hr.

The average speed for the entire trip is 25 km/hr.
How far, in terms of X, was the entire trip?

Can you finish up? Do you have enough information?

Yes, that's exactly what I meant!! Sorry about that!
Although that's when I get stuck, I can't go past that :/

 

[DaexmaretGigis]

Yes, that's exactly what I meant!! Sorry about that!
Although that's when I get stuck, I can't go past that :/

Nevermind, here's what I got:
20x=30x-1200
10x=1200
x=120
120+80=200
80 being x-40
Which is the correct answer Thanks for clearing it up everyone!!

 

[Steven G]

Nevermind, here's what I got:
20x=30x-1200
10x=1200
x=120
120+80=200
80 being x-40
Which is the correct answer Thanks for clearing it up everyone!!

You never used the fact that the average speed for the entire trip is 25 km/hr. Are you saying that doesn't matter? Why not??

 

[lev888]

You never used the fact that the average speed for the entire trip is 25 km/hr. Are you saying that doesn't matter? Why not??

I'm guessing it was used in the first part of the solution (not posted).

 

[JeffM]

Subscripts will help you here a lot.

[math]d_1 = \text {distance first part}; \ t_1 = \text {time first part};\\ v_1 = \text {average velocity first part};\\ d_2 = \text {distance second part}; \ t_2 = \text {time second part};\\ v_2 = \text {average velocity second part};\\ d_w = \text {whole distance}; \ t_w = \text {whole time};\\ v_w = \text {average velocity for whole trip}.\\[/math]
Now you have labels for everything that is involved in the problem, all nice and orderly.

That seems to be nine unknowns. So you need nine equations. But in this case the problem gives you THREE obvious equations.

[math]v_1 = 30, \ v_2 = 20, \text { and } v_w = 25.[/math]
Plus you have three more equations by the definition of average velocity.

[math]v_1 = \dfrac{d_1}{t_1}, \ v_2 = \dfrac{d_2}{t_2}, \text { and } v_w = \dfrac{d_w}{t_w}.[/math]
We have three more equations to go.

You found [imath]d_2 = d_1 - 40[/imath] on your own.

Is there anything more you can do? What can we say about [imath]d_w[/imath]?

Is it not obvious that [imath]d_w = d_1 + d_2[/imath]?

We need one more equation. Once you see the previous equation, it is pretty easy to see that [imath]t_w = t_1 + t_2[/imath].

Now you have your 9 equations, and the rest is just mechanics, and easy mechanics at that.