solving distance

Question

Henry swam 8 kilometers against the current in the same it took him to swim 16 kilometers with the current. The rate of the current was 1 kilometer per hour. How fast would Henry swim if there were no current?

Answer 1

Henry swam 8 kilometers against the current in the same it took him to swim

16 kilometers with the current. The rate of the current was 1 kilometer per hour.

 

Distance = rate*time

d = rt  ...   t = d/r

 

Let r = swim rate with no current

 

Against current the rate is r-1:

t = 8/(r - 1)

 

With the current rate is r+1

t = 16/(r+1)

 

Since the times are the same set the 2 equal to each other

and solve for r

 

8/(r - 1) = 16/(r+1)

8/(r-1) - 16/(r+1) = 0

Common denominator will be (r-1)(r+1) = r²-1

Multiply 8/(r-1) by (r+1)/(r+1)

Multiply 16/(r+1) by (r-1)/(r-1)

 

[8(r+1)]/(r²-1) - 16(r-1)]/(r²-1) = 0

 

[8(r+1)-16(r-1)]/(r²-1) = 0

8(r+1)-16(r-1) = 0

8r + 8 -16r +16 = 0

-8r + 24 = 0

-8r = -24

r = 3 km per hour