Let u and v be the velocity of two trains A and B. While overtaking the relative velocity of train A w.r.t B = u -v.
While crossing, the relative velocity of train A w.r.t B = u+ v.
Total distance to be travelled by car A while crossing = 100 + 100 = 200
So,
Wind is blowing west to east along two parallel tracks. Two trains moving with the same speed in opposite directions have the same steam tracks, if one is double than the other, what is the speed of each train?
Let v and w be the velocity of each train and wind respectively.
According to the question, we have
(v+w) = 2 (v-w)
That is, velocity of each train is 3 times the velocity of wind.
Let be the velocity of rain and be the velocity of the woman. To the woman the rain will appear to come from the direction of Therefore, woman should hold the umbrella in the direction of which is given by
i.e. she should hold the umbrella at an angle south of vertical.
Let s be the total distance travelled by body.
If t1 is the time taken to cover first one-third distance, then
Let t2 be the time for each of the remaining two journeys.
Then,
Therefore,
Average velocity =
=
To the boy waiting at bus stop, the rain will appear to fall in the direction of the resultant of rain and wind.
Let θ be the angle which the resultant velocity subtends with the vertical.
From the figure
∴ Boy should hold the umbrella at angle North of vertical.