Question

A bus starts from Aundh at 1pm and heads towards Swargate at a uniform speed. At 1:30pm, a car starts from Swargate and heads towards Aundh at a uniform speed. Somewhere along the way, the bus and car cross each other. Then, the bus reaches Swargate and the car reaches Aundh, both at 2pm. How many minutes had the car been traveling when it crossed the bus?

Answer 1

let the bus and car moves with the speed Vband Vc respectively in opposite direction, and also let they meet to each other at any point C after travelling distance s1 and s2 in times different times t1 and t2.
then,
distance travelled by bus = distance travelled by car
AC = CA = S1..................(1)
|---------------------S-----------------------|
A.........................C.................................B
[ S1 ] [ S2 ]
hence,
speed of bus Vb =( S/3600) m/s
SIMILARLY, speed of car = Vc = (S/1800)m/s
(since speed of car and bus remains constant throughout the motion.) Now, FROM (1),
Vb×t1 = Vc × t2
(S/3600)×t1 = S/(1800)×t2
hence, -----------------
t2 = t1/2
--------------------
means car takes half of the time taken by bus .