Math Question, I need help

Question

from point A and B, the distance between which is is 30km, two people heading toward each other that left at the same time meet in 3 hours and 20 min. If the first person where to leave 2 hours ahead the other, then they would have met in 2.5 hours after the second person had left. What is the speed of the tow people

Answer 1

If person A starts from the origin on the x axis and person B starts from 30 km on the x axis, then

Let V_A = velocity of person A and V_B = velocity of person B and let t = time

Case1: Distance A = V_A x t The x coordinate is (V_A)t

Distance B = V_B x t The x coordinate is 30 - (V_B)t

Substituting numbers and equating the x coordinates, we have (using 3.33 hours for t)

(VA)t = 30 - (VB)t or 3.33VA + 3.33VB = 30

Case 2: Distance A = 2(V_A) + (V_A)t x coordinate = 2(V_A) + (V_A)t

Distance B = (V_B)t x coordinate = 30 - (V_B)t

Substituting numbers and equating the x coordinates, we have (using 2.5 hours for t)

2(V_A)t + (V_A)t = (V_B)t or 4.5(V_A) + 2.5(V_B) = 30

Now with the 2 equations (in bold), we solve these 2 simultaneous equations to get

V_A = 6.15 km/hr

V_B = 2.25 km/hr