Julie and Eric row their boat (at a constant rate)

Question

Julie and Eric row their boat (at a constant speed) 16 miles downstream for 2 hours, helped by the current. Rowing at the same rste, the trip back against the current takes 8 hours. Find the rate of the current. 

Answer 1

The distance formula is   distance = rate*time  or   d=rt

 

When going downstream the rate of speed was rowing speed 'r'

plus the speed of the current 'c'

 

When returning against the current the rate of speed was the

rowing speed 'r' minus the current 'c'

 

Downstream:   16 = 2(r+c)     distance = (2 hrs)(rate)

Upstream:       16 = 8(r-c)      distance = (8 hrs)(rate)

 

We have two simultaneous equations from which we can find the information

 

2(r+c) = 16

8(r-c) = 16

 

We can divide out the 2 in equation 1 and the 8 in equation 2

 

r+c = 8

r-c = 2      add the two equations together

-----------

2r = 10

r = 5

 

They row at a rate of 5 mph

 

r-c=2

5-c=2

c = 3

 

The rate of the current is 3 mph

 

Check:  2(r+c)=16           8(r-c)=16

            2(5+3)=16          8(5-3)=16

                16 = 16              16=16

 

Our answer fits both equations.

 

Hope this helps.  Good luck with your class.