Answer: the paddling speed is 450 yards per hour.
The speed of the ocean current is 150 yards per hour.
Step-by-step explanation:
Let x represent the paddling speed.
Let y represent the speed of the ocean current.
To go to a beach party 600 yd away, you kayak against the ocean current for 2 h. This means that the total speed at which you kayaked is (x - y) yards per hour.
Distance = speed × time.
Distance travelled while going to the party is expressed as
600 = 2(x - y)
Dividing through by 2, it becomes
300 = x - y - - - - - - - - - - -1
The trip back takes 1 h. Assuming you traveled with the ocean current. The total speed at which you returned is (x + y) yards per hour. Distance travelled while going to the party is expressed as
600 = 1(x + y)
600 = x + y - - - - - - - - - -2
Adding equation 1 to equation 2, it becomes
900 = 2x
x = 900/2
x = 450 yards per hour
Substituting x = 450 into equation 2, it becomes
600 = 450 + y
y = 600 - 450
y = 150 yards per hour
