Question

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 15km/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.)

Answer 1

Answer:22 min

Step-by-step explanation:

we need to find the closest distance between two ship.

let us take the ships meet after time t

now distance travel by first ship at any time t is given by 20t

the position of second ship is 15-15t

let us take distance between them is d

therefore

$D^2=\left ( 20t\right )^2+\left ( 15-15t\right )^2$

now to get the shortest distance differentiate D w.r.t time

$D^2=625t^2-450t+225$

$\frac{\mathrm{d}D }{\mathrm{d} t}=1250t-450=0$

t=0.36hr

thus at $t=0.36hr \approx 21.6min\approx 22 min$