Question

Two train start at the same time from two stations and proceed towards each other with speeds $40$ km per hour and $45$ km per hour respectively. When they meet, it is found that one train has travelled $40$ km more than other. Find the distance between the two stations.

• A. $360$ km
• B. $680$ km
• C. $720$ km
• D. $550$ km

Answer 1

Answer: (B)

$680$ km

Solution:
Given Train starts at the same time.
Hence, Time remains constant.
Speed of Train 'T1' be 'S1' = $40$ km\hr
Speed of Train 'T2' be 'S2' = $45$ km\hr
Let $X$ be the distance at which trains meet.
Train T2 travels $X+40$ km more than Train T1
According to the formula.
$Speed=\frac{Distance}{Time}$
$Time=\frac{X+40}{45}$
$Time=\frac{X}{40}$
From above two equations.
$\frac{X}{40}=\frac{X+40}{45}$
$45\times X=40\times X+40\times 40$
$5\times X=1600$
=$320$ km
Distance between two Stations = $Distance$ at which train T1 meet + $Distance$ at which Train T2 meet + $Distance$ train T2 travels
= $320+320+40$
= $680$