# What time will they meet if they both start at noon, one from A and the other from B?Ann left town A at noon in her car and went down to town B. One hour later, Bill left town B in his car and went...

What time will they meet if they both start at noon, one from A and the other from B?

Ann left town A at noon in her car and went down to town B. One hour later, Bill left town B in his car and went to town A using the same road. Ann and Bill met each other  at 4pm. Next day Bill left town A at noon and went back to town B. Two hour later Ann left town B and went to town A. This time Ann and Bill met at 5pm. Both Ann and Bill always travel at their own constant speeds. What time will they meet if they both start at noon, one from A and the other from B?

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

Let the distance between two cities be X. Let the velocity of Ann is `V_1` and velocity of Bill be` V_2` .

Distance = Velocity*time

When they meet other both of them have travelled X distance. In the first day Ann starts her journey at 12pm and bill do the same in the second day.

For the first day;

`V_1*4+V_2*3 = X` -----(1)

For the second day;

`V_1*3+V_2*5 = X` -----(2)

If they starts simultaneously and if they meet at time t

`V_1*t+V_2*t = X` ----(3)

(1)*5-(2)*3

`11V_1 = 2X`

`V_1 = 2X/11`

(2)*4-(1)*3

`11V_2 = X`

`V_2 = X/11`

From (3)

`t(V_1+V_2) = X`

`t = X/(V_1+V_2)`

`= X/(X/11+2x/11)`

`= 11/3`

So it will take 11/3 hours to meet each other. So they will meet at 3:40pm.