A rowing team rowed their boat 12mi upstream in 1 and 3/4 hours. They made the return trip downstream with the same current in 1 hour. Find the rate of the curr

Question

the question didn't let me finish but the last word is current and if someone can show me a simple way to do this I will appreciate it 

Answer 1

The basic equation is Distance = Rate times Time 

 

Let R = rowing rate in still water

Let C = rate of the current 

 

The upstream rate is R - C and the downstream rate is R + C 

The Distance D = 12 mi is the same in both cases 

So the 2 equations are 

 

12 = (R - C)*1.75 = 1.75*R - 1.75*C    upstream

12 = (R + C)*1 = R + C                       downstream  

 

Multiply the 2nd equation by 1.75 and then add the 2 equations together  

 

12 = 1.75*R - 1.75*C

21 = 1.75*R + 1.75*C

 

33 = 3.5*R + 0*C

R = 33/3.5 = 66/7 

 

Plug this value in for R in the downstream equation and solve for C

 

12 = 66/7 + C

84 = 66 + 7*C

7*C = 18

C = 18/7 mi/hour is the rate of the current 

 

Check:  Upstream rate = 66/7 - 18/7 = 48/7 mi/h so to go 

            12 miles would require 12 / (48/7) = 12*(7/48) = 7/4 = 1 and 3/4 hours  

             Downstream rate is 66/7 + 18/7 = 84/7 = 12 mi/h so to go 12 mi would require 1 hour