Solve.
-A boat moves 10 kilometers upstream in the same amount of time it moves 18 kilometers downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in still water.
A) $31 \frac { 1 } { 2 }$ kilometers per h kilometers per hour
B)9 kilometers per hour
C) $11 \frac { 1 } { 4 }$ kilometers per hour
D) $22 \frac { 1 } { 2 }$ kilometers per h kilometers per hour

Question

Quizplus · Accepted Answer

Let the rate of the boat in still water be $x$ kilometers per hour.Then, the rate of the boat upstream = $x - 9$ kilometers per hourAnd, the rate of the boat downstream = $x + 9$ kilometers per hourGiven that, the boat moves 10 kilometers upstream in the same amount of time it moves 18 kilometers downstream.Therefore, $\frac{10}{x - 9} = \frac{18}{x + 9}$$\Rightarrow x^2 - 81 = 162$$\Rightarrow x^2 = 243$$\Rightarrow x = \pm 15.6$Since the rate of the boat cannot be negative, therefore, $x = 15.6$ kilometers per hourHence, the rate of the boat in still water is $15.6$ kilometers per hour, which is closest to $15 \frac{1}{2}$ kilometers per hour.

Solve -A Boat Moves 10 Kilometers Upstream in the Same 311231 \frac { 1 } { 2 }3121​

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-A Boat Moves 10 Kilometers Upstream in the Same $31 \frac { 1 } { 2 }$