Question 822768: a sail boat goes downstream for an hour and upstream for 3 hours. a motorboat goes downstream 2 hours and upsteam for 1 hour. the river's current speed is 5 mph. the distance traveled by both, not each, boats upstream is 205 miles and downstream is 200 miles find the speed of each boat.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a sail boat goes downstream for an hour and upstream for 3 hours.
a motorboat goes downstream 2 hours and upsteam for 1 hour.
the river's current speed is 5 mph.
the distance traveled by both, not each, boats upstream is 205 miles and downstream is 200 miles find the speed of each boat.
:
Let s = still water speed of the sailboat
then
(s+5) = sailboat speed downstream
and
(s-5)= sailboat speed upstream
:
let m = motorboat speed in still water
then
(m+5) = motorboat speed down stream
and
(m-5) = it's speed upstream
:
Down stream dist equation
1(s+5) + 2(m+5) = 200
s + 5 + 2m + 10 = 200
s + 2m = 200 - 15
s + 2m = 185
s = (185-2m); use for substitution
:
Upstream dist equation
3(s-5) + 1(m-5) = 205
3s - 15 + m - 5 = 205
3s + m = 205 + 20
3s + m = 225
Replace s with (185-2m)
3(185-2m) + m = 225
555 - 6m + m = 225
-5m = 225 - 555
-5m = -330
m = -330/-5
m = +66 mph is the motor boat speed in still water
:
s = 185 - 2(66)
s = 53 mph is the sailboat speed, impossible but there it is
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