Question

Question 6
Luiza kayaks from her house to visit her friend Fernando, who lives 16.2 miles downriver. On her way to Fernando’s house, traveling with the current, the trip takes her an hour and a half. The trip back home takes 13 and a half hours. What is the speed of the current, in miles per hour?

(Suppose that Luiza paddles at the same speed and the river moves at the same speed for both the trip to the park and the trip home.)

Answer 1

since time = distance/speed, if
she paddles at p mi/hr
and the current flows at c mi/hr
then
16.2/(p+c) = 3/2
16.2/(p-c) = 27/2
Now just solve for c

Answer 2

man how you gonna give the answer without giving us the answer we want

Answer 3

Not a very useful answer

Answer 4

I apologize. Here is the full solution:

Let's denote the speed of Luiza as $p$ and the speed of the current as $c$.

Using the formula $d = rt$ (distance equals rate times time), we can write two equations based on the two different trips:

$\text{downstream: } 16.2 = (p+c)\cdot \frac{3}{2}$

$\text{upstream: } 16.2 = (p-c)\cdot 13.5$

Simplifying the first equation, we get:

$16.2 = \frac{3}{2}p + \frac{3}{2}c$

Multiplying both sides by 2/3, we get:

$10.8 = p+c$

Simplifying the second equation, we get:

$16.2 = 13.5p - 13.5c$

Dividing both sides by 13.5, we get:

$1.2 = p - c$

Now we have two equations:

$10.8 = p+c$

$1.2 = p - c$

We can add these equations to eliminate $c$:

$12 = 2p$

$p= 6$

Substituting this value of $p$ into either equation gives us:

$10.8 = 6+c$

$c = 4.8$

Therefore, the speed of the current is 4.8 miles per hour.