the displacement vector from L to S is given by:
Position of S - Position of L
=> [(3t+9)i + (4t-6)j] - [ 18i + 6j ]
LS = (3t-9)i + (4t-12)j
therefore, the time from when DISTANCE, (not displacement), between L and S is 10 km is given by:
LS² = (3t - 9)² + (4t - 12)²
(10)² = 25t² - 150t + 225
0 = 25t² - 150t + 125
t² - 6t + 5 = 0
t = 5 and t = 1
Therefore,
T = 5 or T = 1