AS Mathematics Vector problem?

Question

A balloon flying over flat land reports its position at 7.40am as (7.8,5.4,1.2), the co-ordinates being given in kilometers relative to a check point on the ground. By 7.50am its position has changed to 9.3, 4.4, 0.7). Assuming that it continues to descend at the same speed along the same line, help me find the co-ordinates of the point where it would be expected to land, and the time when this will occur

Answer 1

x = (9.3 - 7.8)/10 t + 7.8

y = (4.4 - 5.4)/10 t + 5.4

z = (0.7 - 1.2)/10 t + 1.2

these would form the parametric equations determining the point coordinates (t would be in minutes .. . . )

x = 0.15t + 7.8

y = -0.1t + 5.4

z = -0.05t + 1.2

the z coordinate would zero at:

t = 1.2/0.05 = 24 (this means after 24 minutes)

at time 8:04am

x = 11.4

y = 3

z = 0