Question

latoya swam 8 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 1 kilometer per hour. how fast would latoya swim if there were no current?
rate she swam with no current: (\boxed{quad}) kilometers/hour

Explanation:

Step1: Define variables

Let \( r \) = Latoya's speed with no current (km/h).
Her speed against current: \( r-1 \) km/h.
Her speed with current: \( r+1 \) km/h.

Step2: Set time equal

Time = distance/speed, so:
$$\frac{8}{r-1} = \frac{16}{r+1}$$

Step3: Cross-multiply to solve

$$8(r+1) = 16(r-1)$$
$$8r + 8 = 16r - 16$$
$$8 + 16 = 16r - 8r$$
$$24 = 8r$$
$$r = \frac{24}{8} = 3$$

Answer:

3 kilometers/hour