Inverse and Direct Variation Word Problems - Examples
Read this topicExplanations 4
- (Video) Algebraic Inverse Proportion by HEGARTYMATHS Thies video by HEGARTYMATHS goes over some word problems based on inverse proportionality. Summary\large{\text{Summary}}Summ…
By Alex Federspiel, Jonathan Heller, Caroline K
- Direct Proportionality in Science Directly proportional variables are used in the sciences. They come up most in the math-y sciences like chemistry and physics (i.e., the scienc…
By Hannah Bonville, Alex Federspiel, Jonathan Heller, Caroline K
- Proportionality: Word Problems Real quick, before we jump into problems. Here are some links in case you need refreshers on any of the topics involved: Direct proportionality: g…
By Hannah Bonville, Alex Federspiel, Jonathan Heller, Anusha Rahman
- (Videos) Variation and Proportionality Word Problems by mathman1024 This video by mathman1024 goes over a word problem based on variation. Summary\large{\text{Summary}}Summary T…
By Alex Federspiel, Jonathan Heller, Anusha Rahman
Problems 52
- A runner got sick for 555 days and couldn't train before a big race. His time for the 800m ended up being 124124124 seconds, 2.52.52.5 slower than his best. If we assume the num…
- Hooke's Law states that the length a spring is stretched lll is directly proportional to the mass mmm by a constant kkk. If a spring with a mass of 333 kg is stretched 999 meter…
- Ohm's law is a law in circuits that states the voltage VVV across a resistor RRR is related to the current III by the equation V=IRV=IRV=IR. If a resistor of 333 ohms has a curr…
- The potential energy, UUU, of a ball in free fall is equal to 12mgh\frac{1}{2}mgh21mgh where mmm is the mass of the ball in kilograms, g=9.8 ms2g=9.8\,\frac{m}{s^2}g=9.8s2m an…
- Is this relationship directly or inversely proportional and what is kkk?
- For the summer, Ben and a bunch of his friends want to rent a beach house for a week. Ben decides to invite 999 friends; they (including Ben) agree to split the cost equally and…
- You want to fence a garden and you have a fixed amount of fencing, but you have not decided what shape you want the garden to be. At first you make an square garden and the leng…
- Because the Olympic swimmer Michael Phelps trains so much, he eats a MASSIVE amount of food. From his breakfasts alone, he eats a total of 56 eggs in one week. Is the relation b…
- Due to the rise of the internet, print magazine companies are hurting. One magazine company is losing an average of 150150150 subscribers a month. Is the relation between the nu…
- When balancing a lever, the amount of weight needed on one side varies inversely with the distance from the fulcrum. If the 300300300 lb weight is 555 feet away from the fulcrum…
- Regarding circuits, the number of equal resistors in series varies inversely to the voltage dropped across them. \\ In the first circuit diagram above, the 1 ohm resistor on the…
- A die has faces numbered from 111 to 666, but weighted so that the probability of rolling the number kkk is directly proportional to kkk. If the probability of rolling a 333 is …
- Two dice appear to be standard dice with their faces numbered from 111 to 666, but each die is weighted so that the probability of rolling the number kkk is directly proportiona…
- 444 people can paint a fence in 333 hours. How long will it take 666 people to paint it? (Assume everyone works at the same rate.)
- Carol spends 171717 hours in a 222-week period practicing her culinary skills. How many hours does she practice in 555 weeks?
- In a shipment of 400400400 parts, 141414 are found to be defective. How many defective parts should be expected in a shipment of 100010001000?
- A rainstorm produced a rainfall of 222 inches per hour. How many hours would it take to get a rainfall amount of one foot?
- How many times more powerful is the radiation intensity at a distance equal to a palm's width, versus the radiation intensity at a distance equal to an arm's length?
- Which elements are inversely proportional? \\ Hint: If two variables are inversely proportional, what do we know about their product?
- You are building a rectangular picture frame. You decided that the area of the frame should be 101010 square feet. What is the relationship between the length and width of the f…
- What's the relationship between how happy Alex is and his hunger level?
- Instead of 222 sticks of butter, Kenny used 333 sticks. How much sugar should Kenny use instead? \\ (note that there are 161616 tablespoons in each cup)
- She counted 606060 pig legs and 909090 chicken legs. Comparing to the amount of pigs, how many more chickens does the farm has?
- The number of meters in a measurement is directly proportional to the number of feet, which is directly proportional to the number of inches. This means that...
- If AAA is directly proportional to BBB, and BBB is inversely proportional to CCC, then...
- If AAA is inversely proportional to BBB, and BBB is inversely proportional to CCC, then...
- If AAA is inversely proportional to BBB, then...
- The stopping distance of a vehicle varies inversely with the friction of the road and it varies directly with the speed that the car is traveling at. When the car is traveling a…
- The frequency of a vibrating string varies inversely with twice its length and directly with its wave velocity. If a string that is 8 feet long has a velocity of 160 meters per …
- The volume of a cylinder varies jointly with the height of the cylinder and the square of its radius. The height of a cylinder is 888 inches, the radius is 222 inches, and the v…
- Keeping this in mind, find the acceleration of a bowling ball that weighs 3.63.63.6 kg and is pushed with a force of 161616 N.
- One topic of interest in physics is kinetic energy. Given the following information, choose the correct equation for kinetic energy. \\ Kinetic energy varies jointly with the ma…
- For years chemists tried to create an equation to describe the relationship between a gas molecule and its environment. Eventually they came up with the Ideal Gas Law. This law …
- The Ideal Gas Equation states that pressure, ppp, and volume, vvv, vary jointly with the number of moles of gas, nnn, the temperature, ttt, and the gas constant rrr. Given the f…
- You weight is defined as: Weight=m×g\text{Weight} = m \times gWeight=m×g where mmm is the mass of your body and ggg is gravity, which of course, is a constant. Which of the foll…
- The speed recorded on the speedometer of a car is: Speed of the car=distancetime it takes to cover the distance\text{Speed of the car} = \frac{\text{distance}}{\text{time it tak…
- The famous equation: E=mc2E = mc^{2}E=mc2 is "Einstein's mass-energy equivalence". EEE is the energy of an object; mmm is the mass of the object; ccc is the speed of light, whic…
- The key to soda keeping its bubbles is the pressure made by the air in the bottle. The equation for pressure is: Pressure=ForceArea\text{Pressure} = \frac{\text{Force}}{\text{Ar…
- The reason roller coasters have that name is because the cars "coast" after the first big hill. This means that the whole ride depends on the cars energy it gets after the first…
- A bike company rents out bikes for tourists at a certain rate. It is 999 dollars to rent the bike for an hour and a half. It is 151515 dollars to rent the bike for two hours and…
- A professor is trying to split her class into groups for a group project. There will be 161616 groups if there are 333 people in each group. How many groups will there be if the…
- Jen is buying freshly made pasta at an Italian market. It is sold by weight at a constant rate. Jen pays 5.65.65.6 dollars for 600600600 grams of fresh pasta. What is the relati…
- Jess is making some lemonade for a school event. She wants to use up all of her 0.20.20.2 liters of lemon concentrate. What is the relationship between the percentage of concent…
- Hooke's Law states that the voltage VVV across a resistor RRR is related to the current III by the equation V=IRV=IRV=IR. A 121212 volt battery is hooked up to a resistor with a…
- In physics, objects in motion have kinetic energy, KEKEKE, that is directly proportional to mass and velocity by KE=12mv2KE = \frac{1}{2}mv^{2}KE=21mv2. If an object with a mas…
- In physics, momentum, ppp, is directly proportional to the mass, mmm, and velocity, vvv, of the object by p=mvp=mvp=mv. If an object of 50 kg50\,kg50kg has a momentum of 2000 kg…
- In physics, momentum refers to the amount of motion something has. Momentum is directly proportional to the velocity as long as the mass is constant. \\ Suppose a car is moving …
- In Physics, a force, FFF, is directly proportional to mass, mmm, and acceleration, aaa, by the equation F=maF=maF=ma. If a force of 121212 N is applied to an object of 3kg3kg3kg…
- The ideal gas law shows that pressure and volume are inversely proportional. Under constant temperature conditions, if a sample of argon gas occupies a volume of 111 liter at a …
- The change in velocity, Δv=v−v0\Delta v = v-v_0Δv=v−v0, is directly proportional to acceleration, aaa, and time, ttt, by Δv=at\Delta v = atΔv=at. If an object starting at rest …
- The distance something falls in freefall is directly proportional to the square of the time it spends falling. \\ Your friend swears he saw someone throw a watermelon so high th…
- From the ideal gas law, we can see that pressure and temperature are directly proportional. A rigid, enclosed container holds a sample of oxygen gas. At 300300300 K (kelvin, an …