SOLUTION: A motorboat left a harbor and traveled to an island at an average rate of 11 knots. The average speed on the return trip was 10 knots. If the total trip took 10.5 hours, how far is

Question 508301: A motorboat left a harbor and traveled to an island at an average rate of 11 knots. The average speed on the return trip was 10 knots. If the total trip took 10.5 hours, how far is the harbor from the island?
Found 2 solutions by Alan3354, oberobic:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The avg speed for the round trip is
2*11*10/(11+10) = 220/21 knots
d = r*t = (220/21)*10.5
d = 110 nautical miles round trip
distance = 55 NM
-----------
55/10 + 55/11 = 10.5 hours as a check

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
d = r*t is the basic distance equation, where d = distance, r= rate, and t = time
.
We have two trips of equal distance here, but we don't know the distance.
.
x = time going to the island
and
11 = rate of speed going to the island
.
We know the two trips took 10.5 hr in total
so
10.5-x = time coming back from the island
and
10 = rate of speed coming back
.
d=d
so
.
11x = 10*(10.5-x)
.
11x = 105 -10x
.
21x = 105
.
x = 105/21
.
x = 5 hr
.
d = 11 * 5 = 55
.
Check using the return trip.
.
10.5 -5 = 5.5
10 * 5.5 = 55
Correct.
.
Answer: The island is 55 knots from the harbor.
.
Note that the unit of measurement 'knots' can mean nautical miles and nautical miles per hr.
In this case, both meanings are knot are used.
.
Done.
RELATED QUESTIONS
A motorboat left a harbor and traveled to an island at an average rate of 15 knots. The... (answered by checkley77)
A motorboat left a harbor and traveled to an island at an average rate of 15 knots. The... (answered by checkley77,josmiceli)
A motorboat left a harbor and traveled to an island at an average rate of 10 knots. The... (answered by Alan3354)
a motorboat leaves a harbor and travels at an average speed of 15 mph toward an island.... (answered by ikleyn)
A ferry leaves a harbor and travels to a resort island at an average speed of 22 mph. On... (answered by richwmiller,drk)
A ferry leaves a harbor and travels to a resort island at an average speed of 22 mph. On... (answered by ewatrrr)
A ferry leaves a harbor and travels to a resort island at an average speed of 22 mph. On... (answered by mananth,amoresroy)
A ferry leaves a harbor and travels to a resort island at an average speed of 22 mph. On... (answered by robertb)
A ferry leaves a harbor and travels to a resort island at an average speed of 22 mph. On... (answered by ankor@dixie-net.com)