Distance Rate Time Dilemma

Thanks guys, but I remain confused.

1.) I understand that relative motion in opp direction, relative velocity being sum of individual speeds.
But why are we using time = distance/sum of their speeds ? Time = Distance/Speed for a given object in motion. Here we are talking about 2 different objects. How can we simply add their speeds ?

2.)fivedaysleft, Yes we could start at the same time say 9 am and walk towards each other. We meet at a given point X. Obviously, we will have covered different distances at different speeds, but the time taken to cover the distances will also be different.
Total distance = 100
Distance 1 : 60 = 6x 10
Distance 2 : 40 = 8 x 5

As you can see, that in above example, different distances and different speeds have different times. So the assumption that they take same time is incorrect.

for 2.)fivedaysleft, Yes we could start at the same time say 9 am and walk towards each other. We meet at a given point X. Obviously, we will have covered different distances at different speeds, but the time taken to cover the distances will also be different.
Total distance = 100
Distance 1 : 60 = 6x 10
Distance 2 : 40 = 8 x 5

the distance covered will be different as you said, but it will be in the ratio of their speeds...
speed(object1) is propotional to distance(object 1)
speed(object2) is propotional to distance(object 2)

or speed1/ speed2 equals distance1/distance 2 = 60/40
and the time remains constant...

now as per 1.) you have to know that relative velocity is v(object1)-v(object2)
consider : a----------------------------------------------------b
d

a moves right to left and b moves left to right ... they cover the distance d
now chose one direction as positive....say left to right
then Va=+v(objecta)
and Vb = -v(objectb) since it is in the opposite direction
so, relative velocity will be Va-Vb = +v(objecta) - [-v(objectb)] = v(objecta)+v(objectb) ie sum of speeds

if you take right to left as positive ie "B" reference relative velocity will be +v(objectb) - [-v(objecta)] which gives v(objectb)+v(objecta) ie sum of speeds

hope it clears your doubt

fivedaysleft, I agree the distance will be proportional to their speeds SHOULD the time be constant. However, that is exactly what my point is. We do not know whether the time is constant. As I put an example up before, for 2 different distances 60 and 40, at different speeds 6 & 8, the time has to be 10 & 5.Clearly the times are NOT same and hence NOT constant. So unless specifically mentioned in the question, we do not know whether the time is same. But answers the both of you gave, you simply assumed the time is same/constant.


I understand that relative velocity will be sum of speeds -question being, why are we calculating time using sum of their speeds. THese are 2 different objects. and the formula is true when specific to an object i.e. for each truck or cycle, D= S x T. We can't just add D= (s1+s2) x T. Thats incorrect.