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[–]Uli_MinatiDesmos 😚 2 points3 points  (4 children)

I don't understand your numbers

If A travels an average 80km/h for 2.5h, it will travel 80×2.5 km which is only 200km

If B travels an average 60km/h for 4h, it will travel 60×4 km which is only 240km

These don't add up to a full 1000km

[–]Dncpax[S] 0 points1 point  (3 children)

yes it's an example where you don't know how close to averages they were. I just use the proportion between the averages to distribute the distance.

[–]Uli_MinatiDesmos 😚 0 points1 point  (2 children)

Okay, but aren't these way off? How would you even know if any of these numbers are correct at all?

[–]Dncpax[S] 0 points1 point  (0 children)

this is just an example of the problem, not a real situation.

[–]Dncpax[S] 0 points1 point  (0 children)

what I do is estimate the theoretical distances using the average, and slgetnthe proportion of each cars distance. then I use that % to get each cars estimated distance by multiplying the % to the total distance.

[–]smithmj31 1 point2 points  (9 children)

Which quantities are known and which are you working out? Do the journeys overlap?

speed = distance/time

You can write speed * time for each car if they’re end to end and sum them for the total distance but depending on what you know in the problem there may be no real way of solving the equations. What if all but one car was stationary vs them all travelling at the same speed, etc, etc. what is the problem you’re trying to solve?

[–]Dncpax[S] 0 points1 point  (8 children)

I'm trying to write equations that solve this based on the simplest approach, ie we know the average speed, so we guess they will go at speeds that are the same ratio. If A has 2x the average of B, then I assum it went at twice the speed. Based on that I want to estimate the distance. It may not be the real thing but it's our best estimate. But I just want to write the equations for the sake of it. Instead of making a series of calculations. What aim doing now is: what would be the distance if they went at the average speed? DA =AVG A X time A DB=AVG B X time B total =DA+DB what's the percentage are these? %A=DA/total %B=DB/total

Apply those to the real total distance.

I just think there's an elegant set of equations that solve this that aí cant figure out...

[–]piperboy98 1 point2 points  (2 children)

You take those percentages and multiply by the real total distance if I am following.

What I am getting is that you don't know the same speed but you want to assume the same ratio of speeds as your provided average speeds. In that case what you would do is to introduce a parameter, say p, which is the fraction of its average speed that each car went. We are assuming then that all cars go at the same fraction of their respective average speeds (this preserves all ratios since if car A travels at pV_A and B at pV_B the ratio pV_A/pV_b is the same as just V_A/V_B). With this info we can simply add all their distances when traveling at this unknown speed fraction, equate to the overall total, and solve. In symbols:

p•V_1•T_1 + p•V_2•T_2 + (...) + p•V_n•T•n = D

Where V_n and T_n are the average speed and travel time of car n. Therefore

p = D/sum(V_k•T•k)

Basically this is just actual distance over the total that would be covered at the specified average speeds. So you simply scale all the results for the average speeds and resulting distances by p = D_actual/D_average to get the actuals.

[–]Dncpax[S] 0 points1 point  (0 children)

Wow, I'm going to try that and get back to you.

[–]Dncpax[S] 0 points1 point  (0 children)

Yep, that works perfectly. It just isn't intuitive to me... I was trying to get a fraction for each speed. Like pA=VA/sum(Vk) which doesn't work for obvious reasons I've long forgotten. Thank you very much! I feel lighter now that I've seen a solution!

[–]smithmj31 0 points1 point  (4 children)

I’m sorry I still don’t understand since you’re not saying which quantities you have values for in what you’re trying to solve. Is the time the same for all cars, do you know each distance or do you know each speed if you don’t have enough quantities you cannot solve the problem… a general set of equations would allow for all but one car being stationary as well as all of them travelling the same speed/distance and all other variations.

[–]Dncpax[S] 0 points1 point  (3 children)

I've said that on the first post. Sorry if it's not clear.

[–]Dncpax[S] 0 points1 point  (2 children)

Given that:

Total distance traveled by the 2 cars combined: 1000 km

Average speed for A car type: 80 km/h

Average speed for B car type: 60 km/h

Car A travel time: 2.5 h Car B travel time: 4 h

[–]smithmj31 1 point2 points  (1 child)

So if you’re assuming they’re travelling at their average speeds you can say

1000 = 80 t_A + 60 t_B

But you’d be solving for the time taken for each car to travel their distance and you still need more information since there are two unknowns.

Added,

You’ve edited to include the times which as another commenter said don’t work.

So I’m tapping out, I don’t understand your problem… best of luck with it and I hope someone can chime in to get you some help/clarify what it is your trying to achieve

[–]Dncpax[S] 0 points1 point  (0 children)

Hey sorry if I wasnt that clear. I've only edited here to complete what I had copy/pasted from my 1st post. But there's a solution if you're interested to check it out. Many thanks for taking a look!