Word Problem please help.?

Average Speed for any journey = Total distance/Total time taken. Here, total time = 7.5 hours (given). Suppose that the one-way distance was d nautical miles, then the time taken for this leg (t1) was d/15 hours, and for the return journey the time was d/10 hours then the total time taken was

d/15 + d/10 = 7.5 hours; multiply both sides of the equation by 30 (the LCM of 10 & 15) to get

2d + 3d = 225 or 5d = 225, so d = 45 miles, and these are nautical miles.

let x = time of first trip

then 7.5 - x = time of return trip

Since the distance has to be the same both way sand d = rt

15x = 10(7.5 - x)

15x = 75 - 10x

25x = 75

x = 3

15(3) = 45

10(7.5 - 3) = 45; distance is 45 nautical miles away

knots is the same as nautical miles per hour. so looking at the total length of time the distance must be the length of time one way multiplied by the rate of knots.

from harbour to island takes 3 hours

island to harbour must take 4.5 hours

3 hours x 15 knots = 45 nautical miles

4.5 hours x 10 knots = 45 nautical miles

total distance travelled is 90 miles, and one way is 45miles.

hope you understand the way i explained it.