Mathematics: 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.

For a portion of the Green River in Utah, the rate

mem8163

21.01.2022

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 = $\frac{\text{Distance traveled}}{\text{speed}}$

= $\frac{5}{(x-4)}$ hours

Time taken to row 5 miles downstream = $\frac{5}{(x+4)}$ hours

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

So $\frac{5}{(x-4)}+\frac{5}{(x+4)}=3$

$5[\frac{x+4+x-4}{(x-4)(x+4)}]=3$

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

10x = 3(x² - 16)

3x² - 10x - 48 = 0

From quadratic formula,

x = $\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

From our equation,

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

Now we plug in these values in the formula,

x = $\frac{10\pm \sqrt{(-10)^{2}-4(3)(-48)}}{2(3)}$

= $\frac{10\pm \sqrt{100+576} }{6}$

= $\frac{10\pm \sqrt{676}}{6}$

= $\frac{10\pm 26}{6}$

= 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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mackenziemelton26

23.02.2021

Step-by-step explanation:

The red number cube has a 1/6 probability of showing a 3 and the blue number cube also has a 1/6 probability of showing a 6.

Just multiply 1/6 times 1/6 to get the probability of both outcomes.

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