Swimming against current, he went 200 meters in 8 minutes. With current, he took 4 minutes. Find current speed and swimmer speed

Question

Swimming against current, he went 200 meters in 8 minutes. With current, he took 4 minutes. Find current speed and swimmer speed

Answer 1

Let the swimmer's speed in still water be x, and the speed of the current be y

 

speed against current = x - y = 200/8 = 25 meters per minute  (speed = distance/time)

 

speed with current is x + y     = 200/4 = 50 meters per minute

 

therefore solving a system of linear equations:

 

x - y = 25     (1)

x + y = 50    (2)

 

(1) + (2) gives 2x = 75; or x = 75/2 = 37.5 meters per minute (swimmers speed)

 

from (2)  y = 50 - x = 50 - 37.5 = 12.5 meters per minute (speed of current)

 

Method 2

 

 

x - y = 25 (1)
x + y = 50 (2)

 

from (1) x = 25 + y   (3)

 

substituting (3) into (2)  25 + y + y = 50

 

25 + 2y = 50; 2y = 50 - 25 = 25; therefore y = 25/2 = 12.5

 

from (1) x - 12.5 = 25, this gives x = 25 + 12.5 = 37.5