Question

A boat travels at a rate of 15 km/hr in still water. It travels 60 km upstream in the same time that it travels 90 km downstream. What is the rate of the current?

(Please help, I don't understand how to set this up.)

Answer 1

Well lets just say the current = R

v=d/t

solve for t

t=d/v

We know that the time will be equal when the boat travels upstream and downstream.

Lets write an equation for the time it takes to go downstream

t=d/v==(90km)/(15km/h + CURRENT)

we must ADD the current to the velocity of the boat in the still water because the stream is helping the boat go faster.

Now do the same thing for the upstream time calculation, except this time you will SUBTRACT the velocity, because the stream is working against the boat.

Now we have two equations and we know that they both take the same amount of time, so set t equal to each other and then you can solve for the current!

Answer 2

I mean to replace the words current with R or another variable :)

Answer 3

Give me a few moments to read this through :)

Answer 4

Wait, so do you mean 90/r+15 = 60r-15 is the equation to solve for r? I did this and I got 75 twice. When I checked the textbook it said three...

Answer 5

hmm yes maybe I did something wrong, let me check

Answer 6

I meant 60/r-15 earlier though.

Answer 7

oh no, you would actually want to subtract the CURRENT, not the speed in still water

Answer 8

and then you will get 3 :)

Answer 9

The problem is, we're trying to find out the current. So we don't know what it is.

Answer 10

we want to solve for R (the current)

Answer 11

So do we subtract d/t?

Answer 12

we don't really care what t is... was is important is that t is EQUAL for both equations (look out for this) because this means that if you find a way to relate both equations to t, you can set them equal to each other

Answer 13

I did get r-15 and r+15 for upstream and downstream.

Answer 14

What did you do? To set up the equation.

Answer 15

actually ignore those negative signs, I don't want you to get confused

Answer 16

the only part you are having trouble with is finding the ACTUAL VELOCITY of the boat.

you are subtracting the speed of the boat in still water from the current.

When the boat goes upstream, we know it can usually travel 15km/hr in still water, but the stream is working OPPOSITE IT! So we can make it negative

(velocity of boat in still water) + (velocity of stream)
= (15km/h) + (-r)

r is negative because it is in the opposite direction of the velocity of the boat

Answer 17

I think I confused you a lot in my original answer, where I said "this time you will subtract the velocity". I should have referred more specifically to the velocity of the current

Answer 18

Do you mean that it should be 15-r, not r-15? Or something along those lines?

Answer 19

yes