Question

"Lashonda swam 4 kilometers against the current in the same amount of time it took her to swim 16 kilometers with the current. The rate of the current was 3 kilometers per hour. How fast would Lashonda swim if there were no current?"

Answer 1

5 km/h

Explanation:

In this problem, Lashonda swam 4 km against the current. So the distance covered in this case is

`d_1=4 km`

Calling
`v` the velocity of Lahonda without the current, and
`c` the velocity of the current, in this situation Lahonda's velocity is

`v-c`

So we can write:

`t_1=(d_1)/(v-c)`

where
`t_1` is the time taken to cover the distance.

When Lashonda swims with the current, her velocity is

`v+c`

So we can write

`t_2=(d_2)/(v+c)`

where

`d_2=16 km` is the distance covered in this case, and
`t_2` the time taken.

The velocity of the current is

`c=3 km/h`

Since Lashonad takes the same time to cover the two distances,

`t_1=t_2`

So we can write

`(d_1)/(v-c)=(d_2)/(v+c)`

And solving for v, we find Lashonda's velocity without the current:

`d_1(v+c)=d_2(v-c)\\d_1 v+d_1c = d_2v-d_2c\\v(d_2-d_1)=c(d_1+d_2)\\v=(d_2+d_2)/(d_2-d_1)c=(16+4)/(16-4)(3)=5 km/h`