Question

The amount of time t (in hours) that it takes to fill a swimming pool varies inversely with the pumping rate r (in kiloliters per hour). The constant of variation is 4. Find how long it will take to fill the pool when the pumping rate is 3.2 kl/hr?

1) 1.25 hours
2) 0.8 hours
3) 12.8 hours
4) 7.2 hours

Answer 1

To find the time it will take to fill the pool at a pumping rate of 3.2 kl/hr given the constant of variation is 4, we use the formula t = k / r, leading to the correct answer of 1.25 hours.

Step-by-step explanation:

The student's question pertains to an inverse variation problem where the amount of time t (in hours) required to fill a swimming pool is inversely proportional to the pumping rate r (in kiloliters per hour). Given that the constant of variation is 4, we can set up the inverse variation formula as t = k / r, where k is the constant of variation, t is the time in hours, and r is the pumping rate in kiloliters per hour.

Plugging in the given values, we get t = 4 / 3.2. When calculated, this yields t = 1.25 hours, which is the amount of time it will take to fill the pool when the pumping rate is 3.2 kl/hr. Therefore, the correct answer from the given options is 1) 1.25 hours.