rate time velocity

Question

A motorboat takes 5 hours to travel 100km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

distance=rate*time

100=(r-c)5 (against the current) where r=rate of the boat and c=rate of the current

100=(r+c)2 (with the current)

the first equation becomes...

20=r-c (divide both sides by 5)

the second equation becomes...

50=r+c (divide both sides by 2)

 

20=r-c

50=r+c

add the equations

70=2r (the c's cancel)

r=35 km/hr for the rate of the boat

substitute into either equation to get...

20=35-c and c=15 km/hr for the rate of the current

50=35+c and c=15 km/hr again

 

Answer 2

Classic algebra 1 problem.

 

Let's call B the rate of the boat and W the rate of the water.  

 

B - W = (100/5) = 20

B = W + 20

 

B + W = (100/2) = 50

 

W + 20 + W = 50

2W = 30 

W = 15

 

B = 15 + 20 = 35

 

Now verify -

 

35 + 15 = 50 kph, so 2 hours downstream.  Check.

 

35-15 = 20 kph, so 5 hours upstream.  Check.