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

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1+1=2

To find the distance between the harbor and the island, we can start by calculating the total time taken for the trip.

Let's assume that the distance between the harbor and the island is represented by 'd' (in nautical miles).

The time taken for the outbound trip can be calculated using the formula:
time = distance / speed.
In this case, the average speed for the outbound trip is 11 knots, so the time taken can be expressed as:
time_outbound = d / 11.

Similarly, the time taken for the return trip can be calculated using the formula:
time = distance / speed.
In this case, the average speed for the return trip is 10 knots, so the time taken can be expressed as:
time_return = d / 10.

Given that the total trip took 4.2 hours, we can find the relation between the time for the outbound and return trips as follows:
time_outbound + time_return = 4.2.

Substituting the expressions for the times of the outbound and return trips:
(d / 11) + (d / 10) = 4.2.

To solve this equation for 'd', we'll find a common denominator and then combine like terms:
(10d + 11d) / (10 * 11) = 4.2.
(21d) / 110 = 4.2.

Next, we'll isolate 'd' by multiplying both sides of the equation by 110:
21d = 4.2 * 110.

Now, divide both sides of the equation by 21 to solve for 'd':
d = (4.2 * 110) / 21.

Evaluating the right side of the equation gives:
d = 220 / 5.
d = 44.

Therefore, the distance between the harbor and the island is 44 nautical miles.