SOLUTION: a boat travels 60 km upsteam in 5 hours. the boat travels the same direction downstream in 3 hours. what is the rate of the boat in still water? what is the rate of the current?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: a boat travels 60 km upsteam in 5 hours. the boat travels the same direction downstream in 3 hours. what is the rate of the boat in still water? what is the rate of the current?      Log On


   

Question 402406: a boat travels 60 km upsteam in 5 hours. the boat travels the same direction downstream in 3 hours. what is the rate of the boat in still water? what is the rate of the current?
Found 2 solutions by checkley79, josmiceli:
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT
D=60*5=300 K. IS THE DISTANCE
300/3=100 K/H IS THE SPEED ON THE RETURN TRIP.
(100+60)/2=40/2=20 K/H IS THE DIFFERENCE IN (CURRENT SPEED.
PROOF:
100-20=80 K/H FOR THE BOAT
60+20=80 DITTO

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!

b+%2B+c = rate going downstream
b+-+c = rate going upstream
------------
given:
upstream:
(1) 60+=+%28b+-+c%29%2A5 km
downstream:
(2) 60+=+%28b+%2B+c%29%2A3 km
------------
This is 2 equations and 2 unknowns
so it's solvable
(1) 5b+-+5c+=+60
(2) 3b+%2B+3c+=+60
Multiply both sides of (1) by 3
and both sides of (2) by 5
Then add the equations
(1) 15b+-+15c+=+180
(2) 15b+%2B+15c+=+300
30b+=+480
b+=+16
Plug this back into (1)
(1) 5%2A16+-+5c+=+60
80+-+5c+=+60
5c+=+20
c+=+4
16 km/hr is the rate of the boat in still water
4 km/hr is the rate of the current
check answer:
(1) 60+=+%2816+-+4%29%2A5 km
60+=+12%2A5
60+=+60
(2) 60+=+%2816+%2B+4%29%2A3 km
60+=+20%2A3
60+=+60
OK