Someone's paddling down a river with a current of 2mph, the first trip took 1.5 hours, the return trip took 2.5 hours. How fast are they paddling

Question

I just need to convert this into numbers

Answer 1

Going downstream the paddling rate, p plus the current, times the time (1.5h) equals the distance. 

 

d=(p+2m/h)*1.5h

 

The distance up stream is the same. Use a time of 2.5h and the current is negative. 

 

d=(p-2m/h)*2.5h

 

Set these distances equal

 

(p+2m/h)*1.5h=

           (p-2m/h)*2.5h

 

multiply out

 

1.5h*p+2*1.5m=

            2.5h*p-2*2.5m

 

combine like terms

 

8m/h=p

 

check your work

d=(8m/h+2m/h)*1.5h=15m

d=(8m/h-2m/h)*2.5h=15m

 

checks out!

Answer 2

 

The distance in each direction is the same.  And distance equals rate multiplied by time.  The time of each leg of the trip is known.  So if you assume that the person is paddling at a constant rate, the only difference is that he/she is paddling with the current on the first leg of the trip, and against the current on the return.  So, you can define two rates, one for each trip:

 

   R₁ = x + 2

 

and 

 

   R₂ = x - 2

 

Then simply solve for x.