Question

Please help. A tourist boat is used for sightseeing in a nearby river. The boat travels 2.4 miles downstream and in the same amount of time, it travels 1.8 miles upstream. If the boat travels at an average speed of 21 miles per hour in the still water, find the current of the river.

Answer 1

time is distance divided by rate
if you call the rate of the current say \(x\) then going downstream the rate is \(21+r\) and going upstream it is \(21-r\)

Answer 2

the distance downstream is \(2.4\) and the distance upstream is \(1.8\) and the times are equal so you can set
\[\frac{2.4}{21+x}=\frac{1.8}{21-x}\] and solve for \(x\)

Answer 3

Okay. So you just solve for x, but what does time matter in the equasion?

Answer 4

Is x the current?

Answer 5

the line in the question "in the same amount of time" is what allows us to set those two expressions for the time equal to each other

Answer 6

ok i wrote something stupid in the first line above
all the \(r\) should be \(x\) i made a typo

Answer 7

Okay, so the equation that you set equal to each other is not effected by the time?

Answer 8

the time is the same, that is why they are equal
it doesn't really matter what the time actually was, it is the same time in either case
of course once you know \(x\) then you know the time, because the time is
\[T=\frac{1.8}{21-x}\]

Answer 9

Thanks for your help. I think I understand it now.