Answer:
Kevin's average swimming speed is 37.5 meters/minutes and speed of the lake's current is 12.5 meters/minutes.
Step-by-step explanation:
Given:- Distance swim by Kevin = 200 metres
Time taken to swim against the lake current= 8 minutes.
Time taken to swim against the lake current=4 minutes.
To find:- average swimming speed of Kevin=?
Speed of the lakes current=?
Solution:-
Let, swimming speed of Kevin be x, and speed of lake current be y.
Therefore,
Speed of Kevin with lake current = x+y ---------------(1)
Speed of Kevin against lake current = x-y --------------(2)
Now formula to calculate speed is,
Speed = [tex]\frac{Distance}{Time}[/tex]
Time[tex]\times[/tex]Speed = Distance
Speed of Kevin with the lake current can be represented as,
Time[tex]\times[/tex]Speed = Distance
[tex]4(x+y)=200[/tex] --------- (from 1 and given)
By dividing above equation with 4 we get,
[tex]x+y=50[/tex] -----------------------(3)
Speed of Kevin against the lake current can be represented as,
Time[tex]\times[/tex]Speed = Distance
[tex]8(x-y)=200[/tex]
By dividing above equation with 8 we get,
[tex]x-y=25[/tex] ---------------------(4)
By adding equation 3 and 4 we get,
[tex]x+y+x-y=50+25[/tex]
[tex]2x=75[/tex]
[tex]\therefore x=\frac{75}{2}[/tex]
[tex]\therefore x=37.5 meters/minutes[/tex] ---------------(5)
Now substituting the value of x from equation 5 in equation 4,
[tex]x-y=25[/tex]
[tex]37.5-y=25[/tex]
[tex]37.5-25=y[/tex]
[tex]\therefore\ y=12.5 meters/minutes[/tex]
As x is the swimming speed of Kevin and y is the speed of lakes current,
Therefore Kevin's average swimming speed is 37.5 meters/minutes and speed of the lake's current is 12.5 meters/minutes.
