SOLUTION: Hi there I'm having trouble solving what I'm sure is a simple equation. A ship is en route and the present speed is 13.5knots. The time is 9am. The distance yet to travel is 215na

Question 921183: Hi there I'm having trouble solving what I'm sure is a simple equation. A ship is en route and the present speed is 13.5knots. The time is 9am. The distance yet to travel is 215nautical miles which will give an arrival time of 0055. I want to arrive at 0600 tomorrow not 0055. I want to know when I can reduce my speed to 8kts to arrive at the intended time.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your current rate of speed is 13.5 knots per hour.
the distance to be covered is 215 knots.
you are starting at 9am.

rate * time = distance
13.5 * time = 215
time = 215/13.5 = 15.92592593 hours.

that will get you into port at approximately 9 + 15.92592593 = 24.92592593 hours from the previous midnight (9am is 9 hours past the previous midnight).

subtract 24 and you will arrive at approximately .92592593 hours which comes out to be roughly 0:55.5555... the next morning.

0055 in the morning is close but not quite right on.

that's not very important to solving this problem, however.

more importantly, you want to arrive at 6:00 am in the morning and you want to know when you can drop your speed to 8 knots per hour in order to do so.

in order to arrive at 6:00 am you need to be traveling 21 hours total.

9 hours past the previous midnight + 21 = 30 hours past the previous midnight.

subtract 24 from that and you get 6am the next morning.

your total travel time needs to be 21 hours.

let x equal the time you are traveling at 13.5 knots.
let y equal the time you are traveling at 8 knots.

you get 2 equations.

x + y = 21 (first equation)
13.5x + 8y = 215 (second equation)

the first equation tells you the total time you traveled.
the second equation tells you the total distance you traveled.

you need to solve these equations simultaneously for x and y.

multiply both sides of the first equation by 8 and you get:

8x + 8y = 168 (first equation after both sides are multiplied by 8)
13.5x + 8y = 215 (second equation)

subtract the second equation form the first to get:

5.5x = 47

divide both sides of the equation by 5.5 to get:

x = 47/5.5 = 470/55 = 94/11

since x + y = 21, this means that y = 21 - 94/11 = 231/11 - 94/11 = 137/11

you have:

x = 94/11
y = 137/11

he will travel 94/11 hours at 13.5 knots and 137/11 hours at 8 knots.

the total distance traveled is 13.5 * 94/11 + 8 * 137/11 = 215 knots.

the total hours traveled = 94/11 + 137/11 = 21 hours.

he starts at 9am the previous morning, travels for 21 hours, and arrives at 6am the next morning.

9 hours past the previous midnight plus 21 hours = 30 hours past the previous midnight equals 30 - 24 = 6 hours part the next midnight which equals 6am the next morning.

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