# A fish can swim 45 miles downriver in the same amount of time that it can swim 27 miles upriver.Find the speed?

Relevance

x = speed of fish

y = speed of current

effective speed dwon river = x+y

effective speed upriver = x - y

rate * time = distance OR

time = distance / rate

time is the same, so set them equal to each other

45/(x+y) = 27/(x-y)

cross multiply

45 (x-y) = 27 (x+y)

you can play with that, but you will not get an actual answer (only a ratio of x and y since you did not specify the time)

18x = 72y

x = 4y

swim speed is four times the current.

NOTE: the swim speed is the midpoint between the upriver and the down river speed, but the problem does not say the time is an hour, it only says the time is the same.

• Find the speed of what? the river or the fish in still water?

r = speed of the river current

f = speed of the fish in still water

45/(f + r) = 27/(f - r)

45(f - r) = 27(f + r)

18f = 72r

f = 4r

The fish's speed is 4 times the speed of the current.

• 36 mph

Because u is the average between (u + v) and (u - v)

(45 + 27)/2 = 36

Regards - Ian