Round clock journey to determine distance

patelsm

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Sep 24, 2017
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hi guys,

Please help me with this. We drew numerous diagrams but still can't work out.

The circular bus drives around Wombourne in a clockwise direction.
it makes four stops on its journey: the supermarket, the church, the school and the maypole.
There are 3500 meters between the supermarket and the school via the church. There are 4750 meters between the church and the maypole via the school.
There are 5230 meters between the school and the supoermarket via the maypole.

How many meters are there between the maypole and the church via the supermarket.

3000m
3525m
3780m
3950m
3980m

answer is 3980m

please help.
saf
 
hi guys,

Please help me with this. We drew numerous diagrams but still can't work out.

The circular bus drives around Wombourne in a clockwise direction.
it makes four stops on its journey: the supermarket, the church, the school and the maypole.
There are 3500 meters between the supermarket and the school via the church. There are 4750 meters between the church and the maypole via the school.
There are 5230 meters between the school and the supoermarket via the maypole.

How many meters are there between the maypole and the church via the supermarket.

3000m
3525m
3780m
3950m
3980m

answer is 3980m

If you were learning algebra, I would suggest this: Call the four distances from one place to the next a, b, c, and d. You can write three equations relating them, using the given facts. These three equations are not enough to solve for four variables; but you just need to find the value of d+a.

Hint: what is a+b+c+d?

Even if you don't know any algebra, this hint should help. What is the total distance around the loop?
 
A = supermarket, B = church, C = school, D = maypole
Draw a circle. Place A,B,C,D on circle in clockwise path.
As DrP says, use a,b,c,d as distances:
a = A to B, b = B to C, c = C to D, d = D to A

"There are 3500 meters between the supermarket and the school via the church."
As example, that becomes:
"There are 3500 meters between A and C".
Which means: a + b = 3500.

Let's see your stuff!!
 
A = supermarket, B = church, C = school, D = maypole
Draw a circle. Place A,B,C,D on circle in clockwise path.
As DrP says, use a,b,c,d as distances:
a = A to B, b = B to C, c = C to D, d = D to A

"There are 3500 meters between the supermarket and the school via the church."
As example, that becomes:
"There are 3500 meters between A and C".
Which means: a + b = 3500.

Let's see your stuff!!


Thank you Denis and DrP: based on your guidance:
A+B = 3500
B+C = 4750
C+D = 5230

So the total distance (round) will be:
=(A+B)+(C+D)
= (Supermarket to School) + (School+ Supermarket)
=(3500) + (5230)
= 8730

i will be really honest, the only way I figured the answer from this point was by 8730 - 3980= 4750 (cheated)
To make sense of this answer, I made myself understand that I have the total "round" distance of 8730 from D to D (Maypole to Maypole), so to find out distance from Maypole to Church which is C+D+A, I have to remove B+C (Church to Maypole). Is this right thinking?

Aint this question a bit to much for under 11s?
 
Thank you Denis and DrP: based on your guidance:
A+B = 3500
B+C = 4750
C+D = 5230

So the total distance (round) will be:
=(A+B)+(C+D)
= (Supermarket to School) + (School+ Supermarket)
=(3500) + (5230)
= 8730

i will be really honest, the only way I figured the answer from this point was by 8730 - 3980= 4750 (cheated)
To make sense of this answer, I made myself understand that I have the total "round" distance of 8730 from D to D (Maypole to Maypole), so to find out distance from Maypole to Church which is C+D+A, I have to remove B+C (Church to Maypole). Is this right thinking?

Aint this question a bit to much for under 11s?

I think you meant to say 8730 - 4750 = 3980.

That's not cheating at all. In fact, algebra is overkill, which is why this is perfectly reasonable for young students. (I don't think you said anything about the context except by putting it under Arithmetic, but that implied it might be a child's question, which is why I phrased my answer in terms of "even if you don't know any algebra".)

The benefit of algebra is that it makes things easier to explain. You found a+b+c+d as (a+b)+(c+d), then found a+d as (a+b+c+d)-(b+c). But you can do the same thing visually. What I initially did, in fact, was to put points A, B, C, D around a circle, draw an arc outside from A to C (which we are calling a+b) and labeled it 3500, and so on. I saw that we could find the total distance around, and that the distance they wanted was all but b+c, and had the answer. The algebra was just to explain it.

[Note that your description above mixes up places (my capital letters) and distances (my small letters). The distance from Maypole (D) to Church (B) is d+a.]
 
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