Question

Going against the current, a boat takes 6 hours to make a 120-mile trip. When the boat travels with the current on the return trip, it takes 5 hours.

What is the rate of the boat in still water?

Answer 1

This is a system of equation problem. One sec but satelite might beat me lol

Answer 2

is it 20?

Answer 3

go ahead i will be quiet

Answer 4

no it is not 20

Answer 5

Oh man!!!

Answer 6

I think I got it...44/2=22!! I did 120/5 and 120/6 added them up and divided them by 2!!

Answer 7

put the rate of the boat in still water as say \(x\) and the rate of the current as \(y\)

Answer 8

hold on'
the average rate is seldom the average of the rates

Answer 9

okay....sorry!

Answer 10

we know that distance equals rate times time , i.e. \(D=R\times T\) and so \(R=\frac{D}{T}\)

Answer 11

yes

Answer 12

if you put \(x\) as the rate of the boat in still water and \(y\) as the rate of the current, then the combined rate with the current is \(x+y\) and against the current it is \(x-y\)
you know the rate with the current is \(\frac{120}{5}=24\) so
\[x+y=24\] and you know the rate against the current is \(\frac{120}{6}=20\)
so
\[x-y=20\]

Answer 13

yes

Answer 14

you solve the two equations
\[x+y=24\]
\[x-y=20\] almost in your head
but if you cannot come up with two numbers that add to 24 and whose difference is 20 then add up the two equations and get
\[2x=44\] and so
\[x=22\]

Answer 15

therefore the boat in still water travels at \(22\) and the current is 2

Answer 16

Awesome!!! Thanks!! Now would xy represent the rate of the boat going with the current?

Answer 17

i do notice that you get the same answer using your method, but i assure you it is a fluke
if you change to 6 hours and 7 hours it would not work this way

Answer 18

It was me doing what I call monkey math!! Just trying everything and anything I could think of!! LOL

Answer 19

\(x+y\) is the rate going with the current, but we already knew that. it was 24

Answer 20

what you wanted was the rate of the boat in still water
it is 22

Answer 21

yes

Answer 22

done
time for the twilight zone
later

Answer 23

thanks!

Answer 24

My take

5(x + y) = 120 // With the Current
6(x - y) = 120 / Against the Current

//With the current
5(x + y) = 120
\[\frac{1}{5} * 5(x + y) = \frac{1}{5} *120 \]
\[x + y = 24 \]

//Against the current
\[ 6(x + y) = 120 \]
\[\frac{1}{6} * 6(x - y) = \frac{1}{6} *120 \]
\[x - y = 20 \]

//Now we have a system
\[x + y = 24 \]
\[x + y = 20 \]

//Eliminate y and add the system
\[x + y= 24 \]
\[x + y = 20 \]

\[2x = 44 \]
\[\frac{2x} {2} = \frac{44}{2} \]
\[x = 22 \]

To find y, which is the current insert 22 into the equation for with the current
\[22+ y = 24 \]
\[ y = 24 -22 \]
\[ y = 2 \]

The current is 2

Answer 25

Made a boo boo the system should of been
\[ x+y=24 \]
\[ x-y=20\]