Question

While on vacation, Kevin went for a swim in a nearby lake. Swimming against the current,

it took him 8 minutes to swim 200 meters. Swimming back to shore with the current took
half as long. Find Kevin's average swimming speed and the speed of the lake's current.
Kevin's average speed:
m/min
Speed of the lake's current:
m/min

Answer 1

Kevin's average swimming speed is 37.5 meters/minutes and speed of the lake's current is 12.5 meters/minutes.

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 =
`(Distance)/(Time)`

Time
`*`Speed = Distance

Speed of Kevin with the lake current can be represented as,

Time
`*`Speed = Distance

`4(x+y)=200` --------- (from 1 and given)

By dividing above equation with 4 we get,

`x+y=50` -----------------------(3)

Speed of Kevin against the lake current can be represented as,

Time
`*`Speed = Distance

`8(x-y)=200`

By dividing above equation with 8 we get,

`x-y=25` ---------------------(4)

By adding equation 3 and 4 we get,

`x+y+x-y=50+25`

`2x=75`

`\therefore x=(75)/(2)`

`\therefore x=37.5 meters/minutes` ---------------(5)

Now substituting the value of x from equation 5 in equation 4,

`x-y=25`

`37.5-y=25`

`37.5-25=y`

`\therefore\ y=12.5 meters/minutes`

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.