Word Problem please help.?
A motorboat left a harbor and taveled to an island at an average rate of 15 knots. The average speed on the retrn trip was 10 knots. If the total trip took 7.5 hours, how many nautical miles is the kharbor from the island?
A motorboat left a harbor and taveled to an island at an average rate of 15 knots. The average speed on the retrn trip was 10 knots. If the total trip took 7.5 hours, how many nautical miles is the kharbor from the island?
?
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.
Douglas
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
Tessibear
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.