Micah rows his boat on a river 4.48 miles downstream, with the current, in 0.32 hours. He rows back upstream the same distance, against the current, in 0.56 hours. Assuming his rowing speed and the speed of the current are constant, what is the speed of the current?

The speed of the current that Micah rows his boat on would be 3 miles per hour assuming that he is rowing 4.48 miles downstream with the current, in 0.32 hours.

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codiepienagoya codiepienagoya · Answer 2 · 2021-12-02T12:35:41+01:00

Following are the calculation for the speed:

Let y become the speed of a river and x be the velocity of Micah's sailing. Then

[tex]\fracd{4.48}{(x + y)}= 0.32\\\\\fracd{4.48}{(x - y)}=0.56\\\\\to 0.32x + 0.32y = 4.48 \ \ \ \ \ \ \ \ \ \ \ \ \ (1)\\\\\to 0.56x - 0.56y = 4.48 \ \ \ \ \ \ \ \ \ \ \ \ \ (2)\\\\(i) \ \ \ x7 \to 2.24 x + 2.24 y = 31.36 \ \ \ \ \ \ \ \ \ \ \ \ \ (3)\\\\(ii) \ \ \ \ x4 \to 2.24x - 2.24y = 17.92 \ \ \ \ \ \ \ \ \ \ \ \ \ (4)\\\\[/tex]

subtracting (3) - (4)

[tex]\to 4.48y = 13.44\\\\\to y = \frac{13.44}{4.48}\\\\\to y = 3[/tex]

From (1):

[tex]\to 0.32x + 0.32(3) = 4.48\\\\\to 0.32x = 4.48 - 0.96 = 3.52\\\\\to x = \frac{3.52}{0.32} = 11\\\\[/tex]

Therefore, the speed is "[tex]\bold{3\ \frac{miles}{hour}}[/tex]".

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