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Shinjini

· started a discussion

· 1 Months ago

How this B & C terms get solved ??? (Question: 89581.0 )

Please explain me the above equation

Question:
Three runners A, B and C run a race, with runner A finishing 24 meter ahead of runner B and 36 meter ahead of runner C, while runner B finishes 16 meter ahead of runner C. Each runner travels the entire distance at a constant speed. What was the length of the race?
Options:
A) 92 meter
B) 96 meter
C) 60 meter
D) 72 meter
E) Can’t be determined
Solution:

Let length of the race be x meter. 

When A runs for x meter, B runs for (x - 24) meters and C runs for (x - 36) meters.

When B run for x meter C runs for (x – 16) meters.

Hence, 

Clearly for B and C

\(⇒ \cfrac{x}{x-16}=\cfrac{x-24}{x-36}\)

⇒ x2 – 36x = x2 – 40x  + 384

⇒ x = 96.

Knowledge Expert

· commented

· 1 Months ago

x/(x−16)=(x−24)/(x−36)

By cross multiplication,

x(x-36) = (x-24)(x-16)

⇒ x2 – 36x = x2 – 16x -24x + 384

⇒ -36x = -40x +384

⇒ -36x +40x = 384

⇒ 4x = 384

⇒ x=384/4 = 96

[Note:- if a/b =c/d then ad=bc]

I hope, it will be very clear to you.....:)
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