algebra question

Question

To go to a beach party 600 yd away, you kayak against the ocean current for 2 h. The trip back takes 1 h. Write and solve a system of equations to find your paddling speed, x, in still water. Find the speed of the ocean current, y.

Answer 1

In both cases the distance is 600 yards

If we assume the ocean current has a speed v and your paddling speed is x we can write

600 = 2x -2v (2 hours total and the current opposes your motion on the way there)

600 = x + v (1 hour total and current helps)

We have two equations. From the 2nd we get x = 600 - v

Plugging this into the first we get

600 = 2(600 - v) -2v

600 = 1200 - 2 v -2v

-600 = -4 v

v = 150 yards per hour

We can now solve for x = 600 - v = 600 - 150

x = 450 yards per hour