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Three runners

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by bluementor » Wed Nov 19, 2008 2:09 am
Three runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, while runner B finishes 8 metres ahead of runner C. Each runner travels the entire distance at a constant speed. What was the length of the race?

A. 36 metres
B. 48 metres
C. 60 metres
D. 72 metres
E. 96 metres

OA: B
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by vishubn » Wed Nov 19, 2008 3:07 am
when A reaches the distance btw B and C is 6m
when B reaches the distance btw B and C is 8m
so ratio is when B covers 12 C covers 10
B:C=12:10
let x b da distance
x-12:x-18=6:5
solve for x
oa 48m

Vishu
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by vishubn » Wed Nov 19, 2008 3:13 am
x-12:x-18=6:5
solve for x
x-12/x-18=6/5

5(x-12)=6(x-18)

5x-60=6x-108

x=108-60
x=48m

Vishu
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by vishubn » Wed Nov 19, 2008 3:14 am
thanks !! For the question !! nice one :)
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by bluementor » Wed Nov 19, 2008 3:40 am
vishubn wrote:
x-12:x-18=6:5
solve for x
x-12/x-18=6/5

5(x-12)=6(x-18)

5x-60=6x-108

x=108-60
x=48m

Vishu
Thanks!
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by jimmiejaz » Wed Nov 19, 2008 5:02 am
vishubn wrote:when A reaches the distance btw B and C is 6m
when B reaches the distance btw B and C is 8m
so ratio is when B covers 12 C covers 10
B:C=12:10
let x b da distance
x-12:x-18=6:5
solve for x
oa 48m

Vishu
Hi vishu,

If i do it another way i get different values. Please correct me.
Lets say distance travelled by c is x
then dist by B is x+6
and A is x+18
Now solving according to the prob..
(x+6)/x = 6/5
we get x=30
what am i missing here. Please correct me.
Shall i find the distance by x+18 since A has finished the race?
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by uttara » Wed Nov 19, 2008 11:54 am
vishubn wrote:when A reaches the distance btw B and C is 6m
when B reaches the distance btw B and C is 8m
so ratio is when B covers 12 C covers 10
B:C=12:10
let x b da distance
x-12:x-18=6:5
solve for x
oa 48m

Vishu
a slight veriation here:
when A reaches the distance btw B and C is 6m
when B reaches the distance btw B and C is 8m
so ratio is when B covers 12 C covers 10

ie to gain 2 meters over C, B needs 12 meters
so to gain 8 meters over C, B will need (12/2)*8=48 meters
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