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 4.2 hours, how far is the harbor from the island?
To find the distance between the harbor and the island, we can use the formula:
Distance = Speed × Time
Let's denote the distance from the harbor to the island as "d" (in nautical miles).
On the outward trip, the motorboat traveled at an average speed of 11 knots, so the time taken for the outward journey can be obtained by dividing the distance by the speed:
Time outward = Distance / Speed outward = d / 11
On the return trip, the motorboat traveled at an average speed of 10 knots, so the time taken for the return journey can be obtained by dividing the distance by the speed:
Time return = Distance / Speed return = d / 10
The total trip took 4.2 hours, so we can write the equation:
Time outward + Time return = Total time
d / 11 + d / 10 = 4.2
To solve this equation for "d," we can first find a common denominator by multiplying 11 and 10:
(10d + 11d) / (11 * 10) = 4.2
Combining like terms in the numerator:
21d / 110 = 4.2
Multiply both sides of the equation by 110:
21d = 4.2 * 110
Simplifying:
21d = 462
Divide both sides of the equation by 21:
d = 462 / 21
Simplifying further:
d = 22
Therefore, the harbor is 22 nautical miles away from the island.