Word problem on speed and current

Question

Phillip left his campsite to a fishing spot 1.8 km downstream. He timed his trip and found that it took 9 minutes. His return trip up stream took 22.5 minutes. Determine the speed of which he paddled and the speed of the river current

Answer 1

distance = rate* time (d = r*t).

 

Let r = the speed of Philip's boat and c = the speed of the current.  Going downstream, with the current, takes 9 minutes:

     1.8 = (r + c)*9

     0.2 = r + c

 

Going upstream, against the current, takes 22.5 minutes:

     1.8 = (r - c)*22.5

     0.08 = r - c

 

Now add the two equations together:

     r + c = 0.20

     r  - c = 0.08

     -------------

     2r = 0.28 km/min

     r = 0.14 km/min = 8.4 km/hr

 

To find c:

     r + c = 0.2

     0.14 + c = 0.2

     c = 0.06 km/min = 3.6 km/hr