8.9 Use direct and inverse variation  (Page 6/10)

The time required to empty a tank varies inversely as the rate of pumping. It took Janet 5 hours to pump her flooded basement using a pump that was rated at 200 gpm (gallons per minute),

1. ⓐ Write the equation that relates the number of hours to the pump rate.
2. ⓑ How long would it take Janet to pump her basement if she used a pump rated at 400 gpm?

The volume of a gas in a container varies inversely as pressure on the gas. A container of helium has a volume of 370 cubic inches under a pressure of 15 psi.

1. ⓐ Write the equation that relates the volume to the pressure.
2. ⓑ What would be the volume of this gas if the pressure was increased to 20 psi?

On a string instrument, the length of a string varies inversely as the frequency of its vibrations. An 11-inch string on a violin has a frequency of 400 cycles per second.

1. ⓐ Write the equation that relates the string length to its frequency.
2. ⓑ What is the frequency of a 10-inch string?

Paul, a dentist, determined that the number of cavities that develops in his patient’s mouth each year varies inversely to the number of minutes spent brushing each night. His patient, Lori, had 4 cavities when brushing her teeth 30 seconds (0.5 minutes) each night.

1. ⓐ Write the equation that relates the number of cavities to the time spent brushing.
2. ⓑ How many cavities would Paul expect Lori to have if she had brushed her teeth for 2 minutes each night?

The number of tickets for a sports fundraiser varies inversely to the price of each ticket. Brianna can buy 25 tickets at $5each.

1. ⓐ Write the equation that relates the number of tickets to the price of each ticket.
2. ⓑ How many tickets could Brianna buy if the price of each ticket was $2.50?

Boyle’s Law states that if the temperature of a gas stays constant, then the pressure varies inversely to the volume of the gas. Braydon, a scuba diver, has a tank that holds 6 liters of air under a pressure of 220 psi.

1. ⓐ Write the equation that relates pressure to volume.
2. ⓑ If the pressure increases to 330 psi, how much air can Braydon’s tank hold?

If $y$ varies directly as $x$ and $y=5,\text{when}x=3.$ , find the equation that relates $x\text{and}y$ .

If $v$ varies directly as $w$ and $v=21,\text{when}w=8.$ find the equation that relates $v\text{and}w.$

If $p$ varies inversely with $q$ and $p=5$ when $q=6$ , find the equation that relates $p$ and $q.$

If $y$ varies inversely with $x$ and $y=11$ when $x=3$ find the equation that relates $x$ and $y.$

If $p$ varies directly as $q$ and $p=10,\text{when}q=2.$ find the equation that relates $p\text{and}q$ .

If $v$ varies inversely with $w$ and $v=18$ when $w=\frac{1}{3}$ find the equation that relates $v$ and $w.$

The force needed to break a board varies inversely with its length. If Tom uses 20 pounds of pressure to break a 1.5-foot long board, how many pounds of pressure would he need to use to break a 6 foot long board?

The number of hours it takes for ice to melt varies inversely with the air temperature. A block of ice melts in 2.5 hours when the temperature is 54 degrees. How long would it take for the same block of ice to melt if the temperature was 45 degrees?