A boat travels 16 miles up the river in the same amount of time it takes to travel 28 miles down the same river. If the current is 3 miles per hour, what is the speed of the boat in still water?
D r t Upstream Downstream
A) 8 miles per hour
B) 3 miles per hour
C) 11 miles per hour
D) 5.5 miles per hour
E) 6 miles per hour

Question

Quizplus · Accepted Answer

Let's denote the speed of the boat in still water as $s$. Then we can create two equations based on the distance, rate, and time formula, using the given information:

For the upstream trip:

$16 = (s-3)t$

For the downstream trip:

$28 = (s+3)t$

Since the problem tells us that the times for each trip are the same, we can set the two equations equal to each other and solve for $s$:

$16/(s-3) = 28/(s+3)$

$16(s+3) = 28(s-3)$

$16s + 48 = 28s - 84$

$12s = 132$

$s = 11$

Therefore, the speed of the boat in still water is $\boxed{	extbf{(C) }11}$ miles per hour.

A Boat Travels 16 Miles Up the River in the Same