Here are the key steps to solve this problem: * Pipe A fills the tank in 3 hours * Pipe B fills the tank in 5 hours * Pipe C drains the tank in 4 hours * With all pipes open, the filling rate (A + B) must equal the draining rate C * Set up an equation: 1/3 + 1/5 = 1/x (where x is time to fill the tank) * Solve the equation: x = 15/4 = 3.75 hours Therefore, the time taken to fill the empty tank with all three pipes open is 3.75 hours.

1. Worksheet for Linear Equation
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1. A biker travels 60 miles in 2.5 hours. Determine the biker's average speed.
2. A car travels between two cities 400 miles apart in 7 hours. The return trip
takes 9 hours. Find the average speed of the car.
3. A police officer, traveling at 100 miles per hour, pursues Philip who has a 30
minute head start. The police officer overtakes Philip in two hours. Find
Philip's speed.
4. A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the
trip, the average speed was 105 mph. Then the tailwind picked up, and the
remainder of the trip was flown at an average speed of 115 mph. For how
long did the plane fly at each speed?

2. 5. An executive drove from home at an average speed of 30 mph to an airport
where a helicopter was waiting. The executive boarded the helicopter and
flew to the corporate offices at an average speed of 60 mph. The entire
distance was 150 miles; the entire trip took three hours. Find the distance
from the airport to the corporate offices.
6. A car and a bus set out at 2 p.m. from the same point, headed in the same
direction. The average speed of the car is 30 mph slower than twice the
speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the
rate of the car.
7. A passenger train leaves the train depot 2 hours after a freight train left the
same depot. The freight train is traveling 20 mph slower than the passenger
train. Find the rate of each train, if the passenger train overtakes the freight
train in three hours.
8. Two cyclists start at the same time from opposite ends of a course that is 45
miles long. One cyclist is riding at 14 mph and the second cyclist is riding at
16 mph. How long after they begin will they meet?

3. 9. A boat travels for three hours with a current of 3 mph and then returns the
same distance against the current in four hours. What is the boat's speed in
calm water? How far did the boat travel one way?
10. With the wind, an airplane travels 1120 miles in seven hours. Against the
wind, it takes eight hours. Find the rate of the plane in still air and the velocity
of the wind.
11. A spike is hammered into a train rail. You are standing at the other end of the
rail. You hear the sound of the hammer strike both through the air and
through the rail itself. These sounds arrive at your point six seconds apart.
You know that sound travels through air at 1100 feet per second and through
steel at 16,500 feet per second. How far away is that spike?
12. John has 20 ounces of a 20% of salt solution. How much salt should he add
to make it a 25% solution?

4. 13. A tank has a capacity of 10 gallons. When it is full, it contains 15% alcohol.
How many gallons must be replaced by an 80% alcohol solution to give 10
gallons of 70% solution?
14. How many pounds of chocolate worth $1.20 a pound must be mixed with 10
pounds of chocolate worth 90 cents a pound to produce a mixture worth
$1.00 a pound?
15. A local grocer has decided to mix 100 pounds of cashews and almonds for a
holiday special. Cashews typically cost $8 per pound and almonds cost $3
per pound. How many pounds of each type of nut must he mix to obtain a
mixture that will cost his customers $5 per pound?
16. A chemist needs a 40% solution of alcohol. He plans to mix 3 liters of a 60%
solution with a 25% solution. How many liters of the 25% solution must we
mix with the 3 liters of the 60% solution to obtain the desired 40% solution of
alcohol?

5. 17. The owner of a coffee shop has decided to mix types of teas to create a new
blend. He will mix a type of tea that sells for $4 per pound with a type that
sells for $2.40 per pound to produce 80 pounds of mixture that he will sell for
$3.60 per pound. How much of the tea that costs $2.40 per pound must he
use in the mixture?
18. How many liters of a 92-octane gasoline should be mixed with 200 liters of a
98-octane gasoline to produce a mixture that is 96-octane gasoline?
19. 2 m³ of soil containing 35% sand was mixed into 6 m³ of soil containing 15%
sand. What is the sand content of the mixture?
20. 9 lbs. of mixed nuts containing 55% peanuts were mixed with 6 lbs. of another
kind of mixed nuts that contain 40% peanuts. What percent of the new
mixture is peanuts?

6. 21. 5 fl. oz. of a 2% alcohol solution was mixed with 11 fl. oz. of a 66% alcohol
solution. Find the concentration of the new mixture.
22. 16 lb of Brand M Cinnamon was made by combining 12 lb of Indonesian
cinnamon which costs $19/lb with 4 lb of Thai cinnamon which costs $11/lb.
Find the cost per lb of the mixture.
23. Emily mixed together 9 gal. of Brand A fruit drink and 8 gal. of Brand B fruit
drink which contains 48% fruit juice. Find the percent of fruit juice in Brand A if
the mixture contained 30% fruit juice.
24. How many mg of a metal containing 45% nickel must be combined with 6 mg
of pure nickel to form an alloy containing 78% nickel?

7. 25. How much soil containing 45% sand do you need to add to 1 ft³ of soil
containing 15% sand in order to make a soil containing 35% sand?
26. 9 gal. of a sugar solution was mixed with 6 gal. of a 90% sugar solution to
make a 84% sugar solution. Find the percent concentration of the first
solution.
27. A metallurgist needs to make 12.4 lb. of an alloy containing 50% gold. He is
going to melt and combine one metal that is 60% gold with another metal that
is 40% gold. How much of each should he use?
28. Brand X sells 21 oz. bags of mixed nuts that contain 29% peanuts. To make
their product they combine Brand A mixed nuts which contain 35% peanuts
and Brand B mixed nuts which contain 25% peanuts. How much of each do
they need to use?

8. 29. John has $20,000 to invest. He invests part of his money at an annual interest
rate of 6%, the rest at 9% annual rate. The return on these two investments
over one year is $1,440. How much does he invest at each rate?
30. Paul made two investments totaling $15,000. The percentage return on the
first investment was 7% annually, while the the percentage return on the
second one was 10% annually. If the total return on the two investments over
one year was $1,350, how much was invested at each rate?
31. Ben invested $30,000, part of which at 5% annual interest rate, the rest at 9%
annual interest rate. The interest earned from the investments was $2,100 at
the end of one year. How much did he invest at each rate?
32. Jason invested $20,000 for one year, Part of his money was invested at an
annual interest rate of 6%, the rest at an annual interest rate of 10%. If his
total income from the two investments over one year was $1,700, how much
was invested at each rate?

9. 33. Jane had $20,000 to invest for one year. She deposited part of which into an
account paying 5% annual interest. the rest into another account paying 8%
annual interest. If the total interest earned at the end of one year was $1,390,
how much was invested at each account?
34. A total of $18,000 was invested for 6 months, part at 4% annual interest rate
and part at 7% annual interest rate. The total interest earned over the 6
month period was $450, how much was invested at each rate?
35. $12,000 was invested for three months. Part of which was invested at 6%
annual interest rate and the rest at 10% annual interest rate. If the total
income for three months from the investments was $240, how much was
invested at each rate?
36. Sue has $15,000 to invest for 5 months, part at 6% annual rate, the rest at
10% annual rate. If the total interest earned at the end of five months is $450,
how much was invested at each rate?

10. 37. Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Castel can dig
the same hole in six hours. How long would it take them if they worked
together?
38. Shawna can pour a large concrete driveway in six hours. Dan can pour the
same driveway in seven hours. Find how long it would take them if they
worked together. It takes Trevon ten hours to clean an attic.
39. Cody can clean the same attic in seven hours. Find how long it would take
them if they worked together.
40. Working alone, Carlos can oil the lanes in a bowling alley in five hours. Jenny
can oil the same lanes in nine hours. If they worked together how long would
it take them?

11. 41. Working together, Paul and Daniel can pick forty bushels of apples in 4.95
hours. Had he done it alone it would have taken Daniel 9 hours. Find how
long it would take Paul to do it alone.
42. Working together, Jenny and Natalie can mop a warehouse in 5.14 hours.
Had she done it alone it would have taken Natalie 12 hours. How long would
it take Jenny to do it alone?
43. Rob can tar a roof in nine hours. One day his friend Kayla helped him and it
only took 4.74 hours. How long would it take Kayla to do it alone?
44. Working alone, it takes Kristin 11 hours to harvest a field. Kayla can harvest
the same field in 16 hours. Find how long it would take them if they worked
together.

12. 45. Krystal can wax a floor in 16 minutes. One day her friend Perry helped her
and it only took 5.76 minutes. How long would it take Perry to do it alone?
46. Working alone, Dan can sweep a porch in 15 minutes. Alberto can sweep the
same porch in 11 minutes. If they worked together how long would it take
them?
47. Ryan can paint a fence in ten hours. Asanji can paint the same fence in eight
hours. If they worked together how long would it take them?
48. Working alone, it takes Asanji eight hours to dig a 10 ft by 10 ft hole. Brenda
can dig the same hole in nine hours. How long would it take them if they
worked together?

13. 49. Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the
job alone she can finish it in 5 hours. If Paul does the job alone he can finish it
in 6 hours. How long will it take for Peter to finish the job alone?
50. A tank can be filled by pipe A in 3 hours and by pipe B in 5 hours. When the
tank is full, it can be drained by pipe C in 4 hours. if the tank is initially empty
and all three pipes are open, how many hours will it take to fill up the tank?