Calculating Average Speed,...for those who appreciate thinking.

[RoverP6B]

As we all I assume drive a car of some description, calculating average speed for a trip could be something that we might like to do every now and then.

So here is a little question to think about and to post your answers to.

"A driver sets out on a journey. For the first half of the distance she drives at the leisurely pace of 60km/h; she drives the second half at 120km/h. What is her average speed on this trip?"

Ron.

[windsock]

Uh OH! :Rolling:

[Slunnie]

80km/h

[clean32]

(60 + 120 ) /2 = 90

unless there is something else

[KarlB]

80 km/hr

[RoverP6B]

80km/h or 90km/h. Two answers but only one of them is correct.

Which one is it? Who would like to change their mind? Who can prove that their answer is the correct one?

Ron.

[vnx205]

Those who misread or misunderstand the question will say 60+120/2=90

Those who read it carefully and realise it doesn't say "travel for half the TIME" rather than "half the DISTANCE" will say 2*60*120/(60+120)=80

[RoverP6B]

That is exactly right vnx205...:)

Equally well done to those who also worked out that 80km/h was the correct answer.

Ron.

[vnx205]

The easiest way I can think of to explain it is with an example.

Imagine the distance to be covered is 120 km.

The first 60 km at 60 km/h will take 1 hour.

The second 60 km at 120 km/h will take half an hour.

The whole trip took one and a half hours.

Speed is distance divided by time.

So 120 km divided by 1.5 hours = 80 km/h

[Slunnie]

Yep, the travel is referenced to distance, not to time.

Sub in a distance eg 100km for the first half, and 100km for the 2nd half.

The first 100km takes 1.66hrs to travel
The 2nd 100km takes 0.83 hours to travel

Total travel time for substituted 200km is 2.5 hours on average.
Average over 100km is then 1.25hours which calculates out to 80km travel for the hour

so 80km/h

[blitz]

what about accelleration from 0 to 60 then 60 to 120 and decelleration from 120 to 0

or am I just being pedantic :D

[vnx205]

The version of that mathematical exercise that I prefer, because I think it makes the point more dramatically is:

If you travel from A to B at 30km/h, how quickly will you have to drive back from B to A to average 60 km/h?

The answer is of course that even travelling at the speed of light will not give you a 60 km/h average because the first leg has already taken all the time needed to do the whole trip at 60 km/h.

For example if A to B was 30 km, it would take an hour to get there and that is how much time you need to average 60 km/h for the 60km return trip.

[RoverP6B]

blitz wrote,...
what about accelleration from 0 to 60 then 60 to 120 and decelleration from 120 to 0

or am I just being pedantic

Hello Blitz,

The question was only simple so the speed is assumed to be constant. Once you start to include acceleration and negative acceleration both linear and non linear, the complexity quickly appreciates.

I can if you like ask some questions where there is considerble complexity,..will keep the brain active and healthy for quite a while...:)

Ron.

[Slunnie]

If you travel from A to B at 30km/h, how quickly will you have to drive back from B to A to average 60 km/h?


To drive bak from B to A to average 60km/h you would only need to drive at 60km/h. :D

Oh you mean... :D

[vnx205]

To drive bak from B to A to average 60km/h you would only need to drive at 60km/h. :D

Oh you mean... :D

:D

I probably became confused when the word "average" came up or maybe I just panicked about how some people might react to the word and forget to conclude the sentence with "60 km/h for the entire trip". :D:D:D

[blitz]

blitz wrote,...

Hello Blitz,

The question was only simple so the speed is assumed to be constant. Once you start to include acceleration and negative acceleration both linear and non linear, the complexity quickly appreciates.

I can if you like ask some questions where there is considerble complexity,..will keep the brain active and healthy for quite a while...:)

Ron.


I was just stirring Ron it's a good question as the answer is not the obvious.

[VladTepes]

I must be dum I dont get it.

If A to b is 30kph and b to a you drive 90 kph wont average kph be 60 ?


(Maths was never a strong point with me )

[Slunnie]

I must be dum I dont get it.

If A to b is 30kph and b to a you drive 90 kph wont average kph be 60 ?


(Maths was never a strong point with me )
If we assume that the distance between each point is 100km, although you can substitute in any distance - the answer will still work out the same.

A->B will take 3.33 hours (30km/h for 100km)
B->C will take 1.11 hours (90km/h for 100km)

The total trip of 200km therefore takes 4.44 hours, simplifying to a 100km trip taking 2.22 hours.

100km / 2.22hours will simplify by dividing the numerator and denominator by 2.22 to:
45km / 1 hour or 45km/h as you know it.




You would be correct however if you drove from A to B at 30km/h for x time and then B to C at 90km/h for x time.

However this question is that you travelled from A to B at 30km/h for x distance and then from B to C for x distance.

[vnx205]

I must be dum I dont get it.

If A to b is 30kph and b to a you drive 90 kph wont average kph be 60 ?


(Maths was never a strong point with me )

Look closely at my example in post #15.

If you drive half the distance at half the speed you want to average, you have already used up all your time.

The key is to look at how much time each half of the trip takes, not how much distance each half of the trip is.

Or consider a more extreme example. You have 60 km to travel. If you drive the first half at 10 km/h, that will take you 3 hours to cover those 30 km, so there is no way you can average 60km/h by driving faster for the rest of the trip. You have already taken 2 hours more than the one hour you would need to do the trip if you wanted to average 60.

Driving at 110km/h will not get your average up to 60 even if (10+110)/2 = 60

[steve_35]

Why do you keep asking maths questions ???????????????????

Are we doing your homework

[vnx205]

Why do you keep asking maths questions ???????????????????

Are we doing your homework

Why do we have a Games Arcade on AULRO?

[vnx205]

Considering the number of people who got those two problems wrong and considering the fact that they are calculations some of us have to do from time to time, I would have thought that the OP has done something quite useful in clearing up a couple of common misconceptions.

He has provided a useful service. :)

[Landy Smurf]

a bit off topic but you guys seem to be quite brainy how good are you guys with logs the maths logs not the wooden type
thanks Tony

[RoverP6B]

steve_35 wrote,...
Why do you keep asking maths questions ???????????????????

Are we doing your homework

Hello Steve,

My homework...not at all. What is the difference in thinking about a mathematics problem or discussing any other topic within this section of the forum?

Thinking about a Mathematics problem, trying to work out a solution can be quite a rewarding exercise, especially if a person learns something that they didn't know along the way. Is that not a good outcome?

This forum I am sure has people from many walks of life, all linked together by an interest in Land Rover etc. We will all have other interests too, some like myself enjoy Mathematics whilst others will like pottery as an example. Areas which may interest one person may not have the same attraction for another, in which case there is no need to leave a comment. I don't post in all sections nor do I comment on all posts, nor do I criticise others for their interests.

Ron.

[Landy Smurf]

maths stimulates the mind

[steve_35]

Im pretty sure my post didn't suggest anything like that or did it suggest this was the wrong place for this question

[RoverP6B]

schmierer LR at singleton wrote,...
a bit off topic but you guys seem to be quite brainy how good are you guys with logs the maths logs not the wooden type
thanks Tony

Hello Tony,

Mathematical logarithms, sure I'll have a shot. What is the question? If I am unable to help, I feel sure that another member will help you.

Ron.

[Landy Smurf]

well i will try and get them up later i am doing them at school and being in a class of 24 i dont get help much and i find myself struggling abit

[RoverP6B]

Hello Tony,

Not a problem, I hope I can be of help to you!

Ron.

[vnx205]

well i will try and get them up later i am doing them at school and being in a class of 24 i dont get help much and i find myself struggling abit

Only 24? :p

How would you have managed in one of my classes in my first year of teaching? In one of them there were 42 students and 36 of them were boys.

That was quite a while ago though. In fact about 23 years before you were born.

Thank goodness things have changed a bit since then. :)

[slug_burner]

logarithms, yes should be able to help.

[slug_burner]

Only 24? :p

How would you have managed in one of my classes in my first year of teaching? In one of them there were 42 students and 36 of them were boys.

That was quite a while ago though. In fact about 23 years before you were born.

Thank goodness things have changed a bit since then. :)

I think 28 was about average when I went through school. Then there was lectures which were given in rooms that could sit over 100.