Ship A is 15 miles east of point P and moving west at 20 mph. Ship B is 60 miles south of point P and traveling north at 15 mph...?

let x be the distance from ship A to point O.

let y be the distance from ship B to point O.

let z be the distance between ship A and ship B.

let t be the time in hours.

x = 15 - 20t

y = 60 - 15t

z = √[(15 - 20t)² + (60 - 15t)²]

z = √[5²(3 - 4t)² + 15²(4 - t)²]

z = 5√[(3 - 4t)² + 9(4 - t)²]

z = 5√(25t²- 96t + 153)

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without calculus:

to minimize this, we can find the least possible value at the vertex of the quadratic inside the radical.

- b / (2a) = 96 / (2*50)

= 48/25

hours.

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with calculus:

dz/dt = 5(25t - 48) / √(25t²- 96t + 153)

to minimize this we set it equal to zero.

we get t = 48/25

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1 and 23/25 hours.

23/25 hours = m/60 minutes.

m = 60(23)/25 = 12(23)/5 = 55.2 ≈ 55 minutes.

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in 1 hour and 55 minutes.

Try using the formula for speed: speed= distance/time. You'll need to set up a series of equations with an X and a Y.