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Explanation:

c = speed of the current

The boat travels at an average speed of 21 mph in still water. When the boat goes downstream, it gets a boost of c mph to get to 21+c mph overall. It travels d = 2.4 miles, so

d = r*t

2.4 = (21+c)*t

t = 2.4/(21+c)

represents the time it takes to go downstream.

For the upstream journey, the boat is slowed down by c mph, so its new speed is 21-c. It travels d = 1.8 miles upstream in the same amount of time t

d = r*t

1.8 = (21-c)*t

1.8 = (21-c)*(2.4/(21+c))

1.8(21+c) = 2.4(21-c)

37.8+1.8c = 50.4-2.4c

1.8c+2.4c = 50.4-37.8

4.2c = 12.6

c = 12.6/4.2

c = 3

The speed of the current is 3 mph

Going downstream, the boat goes from 21 mph to 21+c = 21+3 = 24 mph. It takes t = d/r = 2.4/24 = 0.1 hours = 6 minutes to go downstream.

Going upstream, the boat goes from 21 mph to 21-c = 21-3 = 18 mph. It takes t = d/r = 1.8/18 = 0.1 hours to go upstream.

The fact that we got the same time value t helps us confirm the answer is correct.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

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step-by-step explanation:

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