For a portion of the Green River in Utah, the rate of the river's current is 4 mph. A tour guide can row 5 mi down this river and back in 3 h. Find the rowing rate of the guide in calm water.

Rowing rate of the guide in calm water is 6 mph.

Step-by-step explanation:

Let the rowing rate of the guide is x mph in the calm water.

Rate of river's current = 4 mph

Therefore, speed of the boat upstream = (x - 4) mph

and speed of the river downstream = (x + 4) mph

Time taken to row 5 miles upstream =

                                                             = hours

Time taken to row 5 miles downstream = hours

Since total time spent to row down and come back is = 3 hours

So

5(2x) = 3(x - 4)(x + 4)

10x = 3(x² - 16)

3x² - 10x - 48 = 0

From quadratic formula,

x =

From our equation,

a = 3, b = -10 and c = -48

Now we plug in these values in the formula,

x =

  =

  =

  =

  = 6, -2.67 mph

Since speed can not be negative so x = 6 mph will be the answer.

Therefore, rowing rate of the guide in calm water is 6 mph.

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step-by-step explanation: