A motorboat takes 5 hours to travel 200 km going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Question

perl · Answer

we can use the equation:
distance = rate  * time

anonymous · Answer

Let me try.

200 = r x 5
5/200 = 40
r=40 (Slower)

then 

40-1 = 39 (Faster )

anonymous · Answer

40+1 = 41

anonymous · Answer

Still water rate?

perl · Answer

Let
r = rate of boat in still water
c = rate of river current

For upstream we have :
200 = ( r - c) * 5
Downstream we have : 
200 = ( r + c) * 4

anonymous · Answer

200 = (40-c)*5 (Up stream)
200= (40 + c)*5 (Downstream)

perl · Answer

r is unknown

anonymous · Answer

I thought R -= 40 from my 1st reply

anonymous · Answer

R= 40

Let me try.

200 = r x 5
5/200 = 40
r=40 (Slower)

perl · Answer

see there are actually two unknowns here
the rate of the boat in still water, and the rate of the river stream. 
your equation does not reflect this .

anonymous · Answer

I am so lost..

perl · Answer

go over the equation in my last post above.

anonymous · Answer

ok
..

Let
r = rate of boat in still water
c = rate of river current

For upstream we have :
200 = ( r - c) * 5
Downstream we have : 
200 = ( r + c) * 4

How can I do any more if both r and c are unknown

perl · Answer

we have two equations
upstream 
200 = ( r - c) * 5 
downstream :
 200 = ( r + c) * 4

perl · Answer

we can solve a system of two equations in two unknowns

anonymous · Answer

Up = 40

Down = 50

anonymous · Answer

Not sure I see how that answers rates?

perl · Answer

http://www.wolframalpha.com/input/?i=solve+200+%3D+%28+r+-+c%29+*+5+%2C+200+%3D+%28+r+%2B+c%29+*+4

perl · Answer

They have a step by step solution there. :)

anonymous · Answer

Let
r = rate of boat in still water
c = rate of river current

For upstream we have :
200 = (45 - 5) * 5
Downstream we have : 
200 = ( 45 + 5) * 4

anonymous · Answer

Thank you!!!