5.5 App. of rational/radical functions (in class)

Let [math]x, y[/math] be variables. Suppose [math]x-a[/math] and [math]y-a[/math] have inverse variation. If [math]x=3[/math], then [math]y=-4[/math]; if [math]x=1[/math], then [math]y=8[/math]. Find [math]a[/math].

Luna wanted to knit a sweater for her mom. Working alone, Luna could knit a sweater in 12 hours. When Luna finished half of it, her sister Ines joined her and they finished the rest together. Suppose Luna spent 8.4 hours in total to knit the sweater. How many hours would it take for Ines to knit a sweater alone?

A bottle of plum drink is 500 ml and contains 30% plum juice. If Mia poured half a bottle of plum drink and [math]x[/math] ml of plum juice into his mug, the concentration of plum juice in her drink becomes 50%. What is the value of [math]x[/math]?

(Calculator) The speed of the current in a river was 3 kilometers per hour. An alligator swam 2 kilometers upstream and 2 kilometers downstream in a total of 1.5 hours. What was the speed of the alligator in still water, to the nearest tenth of a kilometers per hour?

An old driver drives from city A to city B with an average speed of 80 km/h. On his return, he drives with an average speed of 90 km/h. What is the old driver’s average speed, in kilograms per hour, for the entire trip?

(Calculator) Working alone, it takes Ethan [math]x[/math] hours to make a Turkish pide. Since Ethan’s sister, Erika, is more professional than Ethan, she can make one 2 hours faster than him. If it takes Ethan and Erika 12 hours to make 10 Turkish pide together, what is the value of [math]x[/math]?

According to the Gas law, the volume [math]V[/math] of a trapped gas varies inversely with pressure [math]P[/math] and directly with temperature [math]T[/math]. ?Which of the following equation is true?

Tanker trucks are used to fill the town swimming pool. Working alone, the pump on the older truck spends 3 more hours to fill the pool than the pump on the newer truck. Suppose they fill the pool in 2 hours working together. How long, in hours, would it have taken the new pump to fill the pool working alone?

According to Newton’s Law of Gravitation, the gravitation force between two planets is directly proportional to the product of their masses, and inversely proportional to the square of the distance separating them. Consider three planets; Planets [math]Mu[/math] and [math]Alpha[/math] have equal masses, while Planet [math]Theta[/math] has twice the mass of Planet [math]Mu[/math]. For which arrangements below will the gravitational force be the greatest?

The load [math]P[/math] (in kilograms) that can safely be supported by a horizontal beam varies directly with the beams’ width [math]W[/math] and the cube of its depth [math]D[/math], and inversely with its unsupported length [math]L[/math]. Show your algebraic work that leads to the answers for the following questions:

If [math]P[/math] does not change, just write “1”.

The Kinetic Energy, [math]E[/math] of an object varies jointly with the mass of the object [math]m[/math] and the square of its velocity [math]v[/math]. If the mass of the object double while the velocity of the object is quartered, find how the kinetic energy changes.