Question

Kahla paddled for 4 hours with a 6-km/h current to reach a campsite. The return trip against the same current took 10 hr. Find the speed of Kahla's canoe in still water.

Answer 1

Hello, thank you for your help!

Answer 2

Let x be the speed in still water. 4(x + 6) is the distance which also equals 10(x -6).

Answer 3

So how do you solve this?

Answer 4

Since each represents the same distance, you can just set these 2 distances equal to each other and get 4(x + 6) = 10(x - 6). Expand each side by the distributive law of multiplication. Get the x terms on one side and the "numbers" on the other. Divide appropriately for x. But the real key to all this is realizing how to get the individual equations for the distances. Unless you ponder a little over the 2 individual equations, the method for solving will be a bit elusive.

Answer 5

It's a must to realize that she is paddling and the current is giving her a push in the first equation, hence the "+". Similarly, for the second equation, the current is a drag, so she is fighting the current and it works against her, hence the "-".

Answer 6

But since you now have the equation, the rest is a snap.

Answer 7

Thank you for your help!

Answer 8

One last thing.

Answer 9

For each of the equations, the first factor is time and the second is rate (each in parentheses), and time multiplied by rate = distance. That's the overall key. Getting equal distances and finding rate.