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

Answer:

5 km/h

Step-by-step 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:

$t_1=\frac{d_1}{v-c}$

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

$t_2=\frac{d_2}{v+c}$

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

$\frac{d_1}{v-c}=\frac{d_2}{v+c}$

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

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