Download Algebra 2: Rational Expressions, Equations, and

Algebra 2: Rational Expressions, Equations, and Functions
Topic F6: Applications | VERSION A Name: ______________________________________________________ 1.
2.
One number is 3 times another. The sum of their reciprocals is 8. Find the numbers. The numbers are and . 5.
One number is 6 times another. The sum of their 6.
reciprocals is !
!"
integers is !
The sum of a number and 2 times its reciprocal is !!
!
!"
!"
. Find the numbers. If a certain number is added to the numerator and denominator of . !
!"
, the result is !
!!
. Find the number. The number added to both is . Find the number. The number is . 4.
. Find the numbers. The numbers are and . 7.
The sum of a number and its reciprocal is !"
The sum of the reciprocals of 2 consecutive odd integers is . Find the numbers. !"
!
The numbers are and . The numbers are and . 3.
The sum of the reciprocals of 2 consecutive 8.
. Find both possible numbers. The numbers are and . The current of a river is 2 miles per hour. A boat travels to a point 6 miles upstream and back in 4 hours. What is the speed of the boat in still water? The speed of the boat in still water is www.varsitylearning.com 1 Algebra 2: Rational Expressions, Equations, and Functions
Topic F6: Applications | VERSION A Name: ______________________________________________________ 9.
Train A has a speed 25 miles per hour greater than that of train B. If train A travels 300 miles in the same times train B travels 225 miles, what are the speeds of the two trains? Train A was traveling at miles per hour where Train B was traveling at miles per hour. 10. A small airplane flies 1040 miles with an average speed of 260 miles per hour. 2 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of the 747? The speed of the 747 was miles per hour. 11. A tour bus normally leaves for its destination at 5: 00 p.m. for a 220 mile trip. This week however, the bus leaves at 5: 20 p.m. To arrive on time, the driver drives 5 miles per hour faster than usual. What is the bus’ usual speed? The bus' usual speed is miles per hour. 12. A water tank can be filled by an inlet pipe in 8 hours. It takes 2 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open? It'll take hours to fill the tank if both pipes are open. 13. It takes 8 hours to fill a pool with the inlet pipe. It can be emptied in 12 hours with the outlet pipe. !
If the pool is full to begin with, how long will it !
take to fill it from there if both pipes are open? It'd take hours to fill the pool if both pipes were open. 14. A sink has two faucets: one for hot water and one for cold water. The sink can be filled by a cold water faucet in 3.9 minutes. If both faucets are open and the sink is filled in 3 minutes, how long does it take to fill the sink with just the hot water faucet open? It'll take minutes to fill the sink with only the hot water faucet open. For the element carbon, 1 mole = 12.01 grams. 15. To the nearest gram, how many grams of carbon are in 2.5 moles of carbon? There are grams of carbon in 2.5 moles of carbon. 16. How many moles of carbon are in 40 grams of carbon, to the nearest hundredth. There are moles of carbon in 40 grams of carbon. www.varsitylearning.com 2 Algebra 2: Rational Expressions, Equations, and Functions
Topic F6: Applications | VERSION A Name: ______________________________________________________ 1.
One number is 3 times another. The sum of their reciprocals is 8. Find the numbers. The numbers are !
!
and !
!
5.
integers is One number is 6 times another. The sum of their reciprocals is !
!"
7.
The sum of a number and its reciprocal is !
. Find the numbers. !"
!"
. Find the numbers. The numbers are 5 and 7 . The numbers are 5 and 30 . 3.
!"
The sum of the reciprocals of 2 consecutive odd integers is . Find the numbers. !"
!
The numbers are 4 and 5 . . 6.
2.
The sum of the reciprocals of 2 consecutive If a certain number is added to the numerator and denominator of . !
!"
, the result is !
!!
. Find the number. The number added to both is 9 . Find the number. !
The number is 5 or . !
8.
4.
The sum of a number and 2 times its reciprocal is !!
!
. Find both possible numbers. The numbers are 9 and !
!
. The current of a river is 2 miles per hour. A boat travels to a point 6 miles upstream and back in 4 hours. What is the speed of the boat in still water? The speed of the boat in still water is 4 mph . www.varsitylearning.com 3 Algebra 2: Rational Expressions, Equations, and Functions
Name: ______________________________________________________ Topic F6: Applications | VERSION A 9.
Train A has a speed 25 miles per hour greater than that of train B. If train A travels 300 miles in the same times train B travels 225 miles, what are the speeds of the two trains? Train A was traveling at 100 miles per hour where Train B was traveling at 75 miles per hour. 13. It takes 8 hours to fill a pool with the inlet pipe. It can be emptied in 12 hours with the outlet pipe. 10. A small airplane flies 1040 miles with an average speed of 260 miles per hour. 2 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of the 747? The speed of the 747 was 520 miles per hour. 14. A sink has two faucets: one for hot water and one for cold water. The sink can be filled by a cold water faucet in 3.9 minutes. If both faucets are open and the sink is filled in 3 minutes, how long does it take to fill the sink with just the hot water faucet open? It'll take 13 minutes to fill the sink with only the hot water faucet open. 11. A tour bus normally leaves for its destination at 5: 00 p.m. for a 220 mile trip. This week however, the bus leaves at 5: 20 p.m. To arrive on time, the driver drives 5 miles per hour faster than usual. What is the bus’ usual speed? The bus' usual speed is 55 miles per hour. 12. A water tank can be filled by an inlet pipe in 8 hours. It takes 2 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open? It'll take 16 hours to fill the tank if both pipes are open. !
If the pool is full to begin with, how long will it !
take to fill it from there if both pipes are open? It'd take 12 hours to fill the pool if both pipes were open. For the element carbon, 1 mole = 12.01 grams. 15. To the nearest gram, how many grams of carbon are in 2.5 moles of carbon? There are 30 grams of carbon in 2.5 moles of carbon. 16. How many moles of carbon are in 40 grams of carbon, to the nearest hundredth. There are 3.33 moles of carbon in 40 grams of carbon. www.varsitylearning.com 4