Question

A ferry makes an 80km trip down the river in 5 hours. The trip back against the current takes 8 hours. Fin the speed of the ferry and the current.

Answer 1

Let's create some variables to help:
f - speed of the ferry
c - speed of the current

So, what's the total (or net) velocity when the ferry is moving with the current. Against the current?

Answer 2

f+c and f-c

Answer 3

OK.
We know that, both ways, it traveled 80km. One way, it took 5 hours, the other way took 8. Do you know the equation for average speed?

Answer 4

D=RxT? Not sure..

Answer 5

Yeah, that's the one.
Let's rearrange it a bit though:

\[speed = \frac{distance}{time}\]

Answer 6

Using that, can you find the average velocity for each direction?

Answer 7

*average speed

Answer 8

80/5 and 80/8

Answer 9

Yup!
Those simplify to 16 and 10.

So, when the ferry is traveling with the current, the speed is 16 km/h, and when it's traveling against the current, the speed is 10 km/h.

Using these numbers, and the equations you found earlier, can you set up a system of equations?

Answer 10

80=16f+c and 80=10f-c?

Answer 11

oh wait nevermind

Answer 12

Im not sure haha

Answer 13

Remember, the first equation (f+c) is the total speed when the ferry is travelling with the current. f-c is when it's travelling against.

This leaves us with:
f + c = 16
f - c = 10

Answer 14

ohh alright, then we use elimination?

Answer 15

Whichever method is easiest for you.

Answer 16

Ok awesome, thanks so much :) you were a big help