Question

two trains start at each other at the same time from station x and y. the train from station x travels with uniform velocity of 100 m/s,while from station y travels with a velocity of 120m/s. the distance between x and y is 3 km .at what distance from station x will the two train meet and after how much time?

Answer 1

Dear Student
Let trains meet at distance d from X station.
$$\begin{gathered} Timetistakenbybothtrainstomeet. \\ Meansdis\tan cediscoveredbytrainfromstationXintimet \\ Insametimetdis\tan ce3000-discoveredbytrianfromstationy. \\ So \\ fortrainfromstationX \\ speed=\frac{dis\tan ce}{time} \\ 100=\frac{d}{t} \\ t=\frac{d}{100} \\ fortrainfromstationY \\ speed=\frac{dis\tan ce}{time} \\ 120=\frac{3000-d}{t} \\ t=\frac{3000-d}{120} \\ Equatingboth \\ \frac{d}{100}=\frac{3000-d}{120} \\ 120d=300000-100d \\ 220d=300000 \\ d=1363.63m=1.36km \\ SofromstationY=3-1.36=1.63km \\ t=\frac{d}{100}=\frac{1363.63}{100}=13.63s \end{gathered}$$
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