A boat leaves a dock at 9:00 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 10:00 pm how many minutes after 9:00 pm were the two boats closest together? round your answer to the nearest minute.

Question

Mathematics

Mcconnell

3 March, 12:47

A boat leaves a dock at 9:00 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 10:00 pm how many minutes after 9:00 pm were the two boats closest together? round your answer to the nearest minute.

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Answers (1)

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Bradley Moreno · Answer 1

after 9:00 P. M. 24 minutes boats were closet together.

Converting speed into km/min

20/60 = (1/3) km/min

15/60 = (1/4) km/min

first boat distance from the dock is d = 1/3 km each minute

Second boat distance from the dock reduced by each minute is

D = 15 - (1/4) * t

d^2 + D^2

= (1/9) * t^2 + (15 - 1/4 * t) ^2

= (1/9) * t^2 + 225 - (30/4) * t + (1/16) t^2

After derivation we get

t=24 minutes