In-a-race-on-a-track-of-a-certain-length-A-beats-B-by-20-m-When-A-was-10-m-ahead-of-the-mid-point-of-the-track-B-was-2-m-behind-it-Find-the-length-of-the-track-in-m-

Question Number 24428 by dhandhaliyachandra@gmail.Com last updated on 17/Nov/17

In a race on a track of a certain length,

A beats B by 20 m . When A was 10 m

ahead of the mid - point of the track B

was 2 m behind it . Find the length of the

track (in m) .

Answered by ajfour last updated on 17/Nov/17

(v_{A} - v_{B}) T = 20; v_{A} T = l

\frac{(l / 2) + 10}{v_{A}} = \frac{(l / 2) - 2}{v_{B}} = (t s a y)

\Rightarrow f r o m f i r s t t w o e q n s .

1 - \frac{v_{B}}{v_{A}} = \frac{20}{l} o r \frac{v_{B}}{v_{A}} = 1 - \frac{20}{l}

u s i n g t h i s i n t h i r d e q n .

\frac{(l / 2) + 10}{1} = \frac{(l / 2) - 2}{(1 - \frac{20}{l})}

\Rightarrow (l + 20) (l - 20) = l (l - 4)

l^{2} - 400 = l^{2} - 4 l

\Rightarrow l = 100 m .

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