5.5 App. of rational/radical functions

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 hour 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 his drink becomes 50%. What is the value of [math]x[/math]?

(Calculator) The speed of the currect 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?

(Calculator) A cable car travels from the bottom to the top of a mountain at a speed of 25 km/h. After staying at the top for 2 minutes, it descends at a speed of 27 km/h. If the entire journey takes 55 minutes, what is the one-way distance of the cable car?

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]?

Working alone, Dr. Ke can weed the garden in 4 hours. His wife Peggy spends the same amount of time to weed the garden when working alone. After they worked together for 1 hour, Mr. Bear helped them to finish in 30 minutes. How long, in hours, would it have taken Mr. Bear to weed the garden by himself?

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?

(Calculator) Mr. Fang drives from Taipei to Tainan with an average speed of 90km/h. On his return trip, he drives with an average speed of 100km/h. What is Mr. Fang’s average speed, in km/h, for the entire trip?

Water can be supplied to the tank through either or both of two pipes. Using the smaller pipe alone, the tank takes two hours longer to fill than if the larger pipes is used alone. Using both pipes, the tank us filled in [math]1\dfrac{7}{8}[/math] hours. How many does it take to fill the tank by the bigger pipe (in hours)?

A traveler drives from Taipei to Tainan with an average speed of 70km/h. On his return, he drives with an average speed of 80km/h. What is the traveler’s average speed, in km/h, for the entire trip?

A traveler drives from Taipei to Tainan with an average speed of [math]\alpha[/math]km/h. On his return, he drives with an average speed of [math]\alpha+10[/math]km/h. What is the traveler’s average speed for the entire trip?

(Calculator) One group of students can set up all 300 desks in the gym in 35 minutes. A second group of students can complete the same task in 45 minutes. Working together, how long will it take the students to set up all 300 desks in the gym? Round to the nearest minute.

(Calculator) Ryan is training for a race. He runs from his house, 5km down the hill, then turns back around and runs 5 km back to his house. Because the return trip is uphill, and he is tired, Ryan’s speed on his return trip is only 80% of his downhill speed. If it takes him a total of 55 minutes to run 10 km, what is Ryan’ s speed, in km/min, going uphill? Round to the nearest 2 decimals.

(Calculator) Jack can assemble five cabinet from Ikea in 3 hours, Jill can assemble the same five cabinets in 4 hours. Working together, how long (in hours and minutes) will it take them to assemble the five cabinets?

(Calculator) Jean rows a boat 6 km downstream, and then turns around and rows the same distance home. The effect of the current on Jean’s boat is 3 km/hr. She spent 4.5 hours in total rowing. What is the speed, in km/hr, of the boat in still water? Round to the nearest hundredth.