1. The problem statement, all variables and given/known data Two straight roads intersect at point O and cross at an angle Θ to one another, such that tan Θ = 3/4.Two cars, A and B are travelling towards O on these roads,A at 5 m/s and B at 8 m/s At a certain moment.A is 100 m from the junction and B, on the other road, is 200 m from the junction. Find (i)the time at which A reaches O (ii) The distance between A and B at this time. (iii) The magnitude and direction of the velocity of A with respect to B (iv) The shortest distance between them. (v)the time at which they are nearest to one another (vi)the time when they are equidistant from O 2. Relevant equations Vab = Va - Vb 3. The attempt at a solution I got every part except (vi) (i) 100/5 = 20 seconds (ii) 200 - 8(20) = 40m (iii) Vab = ( -5(4/5)i -5(3/5)j ) -(-8i) = 4i -3j m/s |Vab| = 5m/s inverse tan 3/4 = 36.87 degrees south of east (iv) 40(sinΘ) = 40(3/5) = 24 m = shortest distance (v) Pythagoras theorem (40^2 -24^2)^(1/2) = 32m 32/5 =6.4 seconds 20 + 6.4 = 26.4 seconds (vi) This is the part im stuck on.I know I need the distance from O when they are equidistant but I just can't seem to think of any way that I could get none of the examples in my book covered this any help would be appreciated.