Habs boys maths 2006 question 30 - help

[Minesh]

A bus goes on a circular route...the cost of traelling between any 2 stops is worked out by adding together the fares be tween consecutive stops eg A to B is 40p and B to C is 37p then A to C is 77p.

the total cost of 1 ticket from G to J and 1 ticket from G to I is £1
'' '' '''' G to J and 1 '' '' H to J is £1.20
'' '' '' '' 1 '' '' G to J, 1 ticket from G to H, and 1 ticket from I to J is £1.30

what is the cost of 1 ticket from G to J?


Many thanks

[workhard]

Hi Minesh! I think the answer is 70p.....Please check that this works!

Just looking at your three journeys, one can deduce that:-

One stop to J is 30p more than one stop to I.
One stop to H is 10p more than one stop to I.

We can now look at each multistop journey you describe in terms of just the cost of one stop to I. Which leads us to establishing that the fare for the one stop to I is 10p. So the overall answer is 20p+10p+40p=70p.

Algebraically (simultaneous equations):

The question tells us that the three journeys are:

H+I+J+H+I=100
H+I+J+I+J=120
H+I+J+H+J=130

From this, we deduce that:

I+30=J
I+10p=H

Substituting these back into the first equation, we get :

5I+50=100
So 5I=50
So I=10 .... so H=20 and J=40 .... so H+I+J=70.

By the way, we did a lot of these papers two years ago. I reckon that very few will get such harder questions right. Some will just apply mental logic and work it out that way..... I wonder if anyone will be able to do it fully algebraically?

Hope this helps.

WH

[Minesh]

I agree wholeheartedly - many thanks for taking the time to respond and explain so clearly.

[mitasol]

There was a long discussion about this question http://www.elevenplusexams.co.uk/forum/ ... ute#p81201" onclick="window.open(this.href);return false;