Anyone good at maths?

stu

Okay heres the story. I wrote my maths matric paper 1 on the 4th (i think) and one of questions has been bugging me ever since.

Here it is:

Tshepang rushed from home to the soccer stadium at 165km.h to see her favourite team. They lost the game so, feeling sad, she drove home taking the same route, at 110km.h
Culculate Tshepangs average speed for the whole trip.
It is not 137.5km.h

I have tried lots of different methods and ideas to get the answer but Im not wining with this one.
Any one have any ideas?

I know if I do get the answer Im going to kick myself for not getting it in the exam.

raithza

To find the average speed, divide TOTAL distance by total time.

so lets say she lives y km away from the stadium:

it took her y/165 hrs to get there, and y/110 hrs to get back.

total time spent on road = y/165 + y/110
total distance = 2y

to find average, calculate: 2y / (y/165 + y/110)

http://www.wolframalpha.com/input/?i=2y/(y/165+%2B+y/110)

?

AlanRatcliffe

But you don't have either distance or time. All you have is the speed there and back. Same route, so the distance is the same anyway.

Math is not my strong suit, but it still seems pretty obvious to me: add the two speeds and divide by two. So the answer is 137.5 km/h.

Wizard

raithza wrote to find average, calculate: 2y / (y/165 + y/110)

= 2y / (y/165 + y/110)
= 2y / ([110y + 165y]/(110x165)]
= 2y / y(110 +165)/(110 x 165)
= 2 / (275/18150)
= 2 x 18150 / 275
= 132

raithza

Alan Ratcliffe wrote But you don't have either distance or time. All you have is the speed there and back. Same route, so the distance is the same anyway.

Math is not my strong suit, but it still seems pretty obvious to me: add the two speeds and divide by two. So the answer is 137.5 km/h.

Thats the trap - remember you spend more time driving the same route at 110km/h than 135km/h

DaFiz

stu wrote It is not 137.5km.h

It is 137.5kmh. You only have two figures to work with and the average is half the total... ?

AlanRatcliffe

raithza wrote Thats the trap - remember you spend more time driving the same route at 110km/h than 135km/h

As I see it, time doesn't enter into it - they want average speed. (Unless they want you to figure out the relativistic effects of the different speeds. ?)

PeteM

What I find disturbing is that in a Matric paper they casually refer to the driver travelling at 45km/h over the speed limit. It's no wonder we see so many deaths on the roads. ☹

Wizard

PeteM wrote What I find disturbing is that in a Matric paper they casually refer to the driver travelling at 45km/h over the speed limit. It's no wonder we see so many deaths on the roads. ☹

Good point Pete ... ?

Here's another way of expressing the same problem.

Suppose the distance is 165km.
- Trip to game takes 1 hour (speed = 165 km/h)
- Trip back takes 1.5 hours (speed = 110 km/h)

Average speed
= total distance / total time
= (165 + 165) / (1 + 1.5)
= 330 / 2.5
= 132

The answer is the same irrespective of the distance.
So the sum gets easier if you just pick an arbitrary distance.

giggsy

If you want my help just let me know...

I got an F Pass in matric on Standard Grade. That's between 33.3 and 35%, so if my calculations are correct, and I am pretty sure that they are, I got 34%. As I said, send me a PM if I can assist.

costafonix

yeh but here's another factor to consider, what if Tshepang decided to stop on the way home and pick up her mate Sipho and detoured past McDonalds? Would the extra weight of the Quarter Pounder and Chips not affect the calculation? OR,,, OR if Sipho had his guitar with him and stuck the neck out the window, what about the drag co-efficient? ? ?

singemonkey

Haha! I was thinking completely on the wrong track. Wizard's got it of course. The trick that Tshepang spent longer travelling at 110 than at 165, and the ratio of time at 110 to 165 is the same no matter the actual distance. And that's what gets you the correct average. To simply add the two and divide by two assumes that the the two speeds were driven for the same length of time.

IceCreamMan

Wizard wrote
PeteM wrote What I find disturbing is that in a Matric paper they casually refer to the driver travelling at 45km/h over the speed limit. It's no wonder we see so many deaths on the roads. ☹
Good point Pete ... ?

Here's another way of expressing the same problem.

Suppose the distance is 165km.
- Trip to game takes 1 hour (speed = 165 km/h)
- Trip back takes 1.5 hours (speed = 110 km/h)

Average speed
= total distance / total time
= (165 + 165) / (1 + 1.5)
= 330 / 2.5
= 132

The answer is the same irrespective of the distance.
So the sum gets easier if you just pick an arbitrary distance.

Simple maths .....

reminds me of the 3 okes that each put in 10 ront ,buy a pizza for 25 ront ...give the waiter a tip of 2 ront etc etc

vic

Alan Ratcliffe wrote
raithza wrote Thats the trap - remember you spend more time driving the same route at 110km/h than 135km/h
As I see it, time doesn't enter into it - they want average speed. (Unless they want you to figure out the relativistic effects of the different speeds. ?)

these are extreeemely interesting....here you factor in time dilation and Lorentz contraction... ? which only become important at speed c

vic

Wizard wrote
PeteM wrote What I find disturbing is that in a Matric paper they casually refer to the driver travelling at 45km/h over the speed limit. It's no wonder we see so many deaths on the roads. ☹
Good point Pete ... ?

Here's another way of expressing the same problem.

Suppose the distance is 165km.
- Trip to game takes 1 hour (speed = 165 km/h)
- Trip back takes 1.5 hours (speed = 110 km/h)

Average speed
= total distance / total time
= (165 + 165) / (1 + 1.5)
= 330 / 2.5
= 132

The answer is the same irrespective of the distance.
So the sum gets easier if you just pick an arbitrary distance.

a very elegant solution....Wizard must be a Math wizz kid... ?

AlanRatcliffe

vic wrote these are extreeemely interesting....here you factor in time dilation and Lorentz contraction... ? which only become important at speed c

Not really, tau becomes more important the closer you get to C, but still has an effect at lower speeds. So I suppose in this case it would depend on how many decimal points you were willing to calculate. ? Hmmm... hadn't even considered L...

[deleted]

Time dilation and Lorentz contraction sounds much like the inverse ratio between water temperature and Speedo embarrassment.

vic

Stratisfear wrote Time dilation and Lorentz contraction sounds like the inverse ratio between water temperature and Speedo embarrassment.

..LOL...particularly in West Coast waters... ?

Marilyn Monroe suggests to Einstein: What do you say, professor, shouldn't we marry and have a little baby together: what a baby it would be - my looks and your intelligence!
Einstein: I'm afraid, dear lady, it might be the other way around... ?

stu

Thanks raithza and Wizard.
Raithza what you said makes perfect sense. Im not trying to find the average between the two numbers.

Kicking myself for not thinking of that >☹

Llewelyn

Alan Ratcliffe wrote Not really, tau becomes more important the closer you get to C, but still has an effect at lower speeds. So I suppose in this case it would depend on how many decimal points you were willing to calculate. ? Hmmm... hadn't even considered L...

Just because I was bored while studying for my physics exam last week, I calculated what my mass would be at 100km/h...the change was so tiny I can't even remember it ?