Aboat leaves a dock at 7: 00 pm and travels due south at a speed of 20 km/h. another boat has been heading due east at 15 km/h and reaches the same dock at 8: 00 pm. how many minutes after 7: 00 pm were the two boats closest together? (round your answer to the nearest minute.) min

22 minutes after 7:00 P.M. they will be closest.

Step-by-step explanation:

A boat heading south travelling for t hours at the rate of 20 km/h, so the distance x = 20t

The another boat will reach the dock after travelling another 1-t hours at the rate of 15 km/h, so the distance =

y = 15 - 15t

D = d²  = x² + y²

D = (20t)² + (15 - 15t)²

dD/dt = -2(15² )( 1-t ) +2 × 20² × t

dD/dt = 2 (15² + 20²) × t -2 ( 15 )² = 0

t =

t = 0.36 hours = 0.36 × 60 = 21.6 minutes ≈ 22 minutes

Therefore, the distance is minimized 22 minutes after 7 pm.