The distance between Ahmedabad and Vadodara is 100 km. Two trains set-off simultaneously from Ahmedabad and Vadodara towards each other. The speed of these trains are 45 `kmh^(-1) and 30 kmh^(-1)` respectively. When will they cross each other ?

Explanation

Speed of train set off from Ahemdabad,
`v_(A) = 45 km h ^(-1)`
Speed of train set off from Vadodara,
`v _(B)( = - 30 km h ^(-1)`
(this train is moving in opposite direction)
`x_(BO) - x_(AO) = 100 km`
When both trins meet, the relative displacement will be zero. i.e., `x _(B) - x_(A) = 0`
`therefore x_(B) - x_(A) = (x _(BO) - x _(AO)) + (v _(B) - v_(A)) t `
`therefore 0=100 + (-30 -45) t`
`therefore 75 t = 100`
`therefore t = (100)/(75) = 4/3` hours.