WorksheetsProblem Solving: Real-life Rational Equations
Total questions: 60
Worksheet time: 45mins
Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.
Problem 1: Two People Painting a House
Alice can paint a house alone in 10 hours, while Bob can do it in 15 hours. How long will it take them to paint the house together?
6 hours
8 hours
12.5 hours
25 hours
Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.
Anna walks at 4 mph and bikes at 12 mph. If she travels 30 miles total and spends the same amount of time walking as biking, how far did she walk?
6 miles
8 miles
10 miles
12 miles
Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.
Problem 3: Fuel Efficiency
A car gets 20 mpg in the city and 30 mpg on the highway. If it travels 500 miles total and uses 20 gallons of fuel, how many miles were driven on the highway?
200 miles
250 miles
300 miles
350 miles
Problem 4: Travel Time A cyclist travels 20 miles. He rides half the distance at 10 mph and the other half at 20 mph. What is his average speed for the entire trip?
13.33 mph
15 mph
12 mph
16 mph
Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.
Problem 5: Filling a Pool with a Leak
A pool can be filled by a pipe in 5 hours, but there is a small leak that empties it in 15 hours. If the pipe is left open and the leak is not fixed, how long will it take to fill the pool?
6 hours
7.5 hours
7 hours
5 hours
Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.
Anna walks at 4 mph and bikes at 12 mph. If she travels 30 miles total and spends the same amount of time walking as biking, how far did she walk?
6 miles
8 miles
10 miles
12 miles
A cyclist travels 30 miles. He rides half the distance at 15 mph and the other half at 30 mph. What is his average speed for the entire trip?
20 mph
22.5 mph
18 mph
25 mph
A car gets 20 mpg in the city and 30 mpg on the highway. If it travels 500 miles total and uses 20 gallons of fuel, how many miles were driven on the highway?
200 miles
250 miles
300 miles
350 miles
A cyclist travels 20 miles. He rides half the distance at 10 mph and the other half at 20 mph. What is his average speed for the entire trip?
13.33 mph
15 mph
12 mph
16 mph
A car travels 120 miles on 4 gallons of fuel. Find the fuel efficiency in miles per gallon (mpg).
20 mpg
30 mpg
40 mpg
15 mpg
A truck travels 80 kilometers in 2 hours. What is the speed of the truck in meters per second (m/s)?
11.1 m/s
22.2 m/s
40 m/s
80 m/s
A student weighs 65 kilograms. Convert their weight to pounds.
143 lbs
120 lbs
100 lbs
180 lbs
A recipe calls for 500 milliliters of water. How many liters is that?
0.05 liters
0.5 liters
5 liters
50 liters
A metal weighs 8000 grams. Convert the weight to kilograms.
8 kilograms
80 kilograms
0.8 kilograms
800 kilograms
A person runs 3 kilometers in 12 minutes. Find the speed in meters per second.
2.5 m/s
4.2 m/s
3.6 m/s
1.8 m/s
A piece of metal has a mass of 0.5 kg and a volume of 100 cm³. Find its density in g/cm³.
0.005 g/cm³
0.5 g/cm³
5 g/cm³
50 g/cm³
A bottle contains 1.5 liters of juice. How many milliliters of juice are in the bottle?
150 milliliters
1500 milliliters
15 milliliters
1050 milliliters
The temperature in Celsius is 25°C. Convert this to Fahrenheit.
77°F
32°F
100°F
50°F
A runner completes a 400-meter race in 50 seconds. Find the runner's speed in kilometers per hour.
28.8 km/h
14.4 km/h
36 km/h
20 km/h
Lena earns 3000permonth.Shespends 900 on rent, 200ongroceriesweekly,and 100 on a gym membership. What does the variable 'x' represent in the expression: B = 3000 - 900 - 200x - 100?
The number of weeks in a month
The number of gym visits
The number of months Lena works
The number of times Lena pays rent
Noah earns 250weekly.Hesaves 100 and uses the rest for bills and personal expenses. What does the expression E = 250 - 100 represent?
The amount Noah spends on bills and personal expenses
The total amount Noah earns weekly
The amount Noah saves weekly
The total amount Noah spends in a month
Sophia earns $18 per hour and works h hours per week. Expression: I = 18h. What does I represent?
Sophia's total weekly income
Sophia's hourly wage
The number of hours Sophia works per week
The amount Sophia saves each week
What does each part of the expression C = 45 + 0.10x represent?
45 is a fixed cost and 0.10x is a variable cost depending on x.
45 is a variable cost and 0.10x is a fixed cost.
Both 45 and 0.10x are fixed costs.
Both 45 and 0.10x are variable costs.
Emma spends 2000monthly: 1000 on rent, 400onfood,and 600 on other expenses. Expression: E = 1000 + 400 + 600. What does the '400' in the expression represent?
Rent
Food
Other expenses
Total expenses
Jack earns $1200 biweekly and saves 20% of it. Expression: S = 0.20 × 1200. What does the number 0.20 in the expression represent?
The total amount Jack earns
The percentage Jack saves
The amount Jack spends
The number of weeks
Olivia spends $60 each week on transportation. How much does she spend in x weeks? What does each part of the expression T = 60x represent?
T is the total amount spent, 60 is the amount spent per week, and x is the number of weeks.
T is the amount spent per week, 60 is the number of weeks, and x is the total amount spent.
T is the number of weeks, 60 is the total amount spent, and x is the amount spent per week.
T is the amount spent per week, 60 is the total amount spent, and x is the number of weeks.
Interpret each part of the expression R = 3000 - 800 - 50x.
3000 is the initial amount, 800 is a fixed deduction, and 50x is a variable deduction depending on x.
3000 is the final result, 800 is added to 50x, and R is the variable.
R is always 3000, 800 and 50x are ignored.
R is the sum of 3000, 800, and 50x.
What does the expression C = 15 + 5x represent in the context of a subscription that costs 15permonthplus 5 per movie rented (x)?
C is the total cost, 15 is the monthly fee, and 5x is the cost for x movies rented.
C is the number of movies rented, 15 is the cost per movie, and 5x is the monthly fee.
C is the monthly fee, 15 is the cost for x movies, and 5x is the total cost.
C is the cost per movie, 15 is the number of movies, and 5x is the monthly fee.
Maya has 2000.Shespends 75 weekly. Expression: B = 2000 - 75x. What does the number 75 represent in the expression?
The total amount Maya has
The amount Maya spends each week
The number of weeks
The balance left after x weeks
Convert 120 inches to feet.
10 feet
12 feet
8 feet
15 feet
Convert 5 kilograms to grams.
5000 grams
50 grams
500 grams
50000 grams
Convert 8 miles to kilometers.
12.87 kilometers
10.00 kilometers
15.00 kilometers
8.00 kilometers
Convert 3 hours to seconds.
10,800 seconds
3,600 seconds
1,800 seconds
21,600 seconds
Convert 50 liters to milliliters.
Convert 20 meters per second to kilometers per hour.
Convert 5000 milligrams to grams.
(a)
Convert 30°F to Celsius using the formula C=(F–32)×5/9. 30°F = ____ °C
-1.11°C
0°C
-10°C
5°C
Convert 200 centimeters to meters.
(a)
Convert 45 pounds to kilograms (1 lb = 0.453592 kg).
The following are the test scores of 8 students in Fin Lit: 85, 85, 90, 88, 95, 78, 72, 91. a) Find the mean, median, and mode of the data.
Mean: 85.5, Median: 86.5, Mode: 85
Mean: 86, Median: 88, Mode: 90
Mean: 84, Median: 85, Mode: 78
Mean: 87, Median: 90, Mode: 91
The following are the test scores of 8 students in Fin Lit: 85, 85, 90, 88, 95, 78, 72, 91. b) Compute the inter-quartile range (IQR).
IQR: 10.5
IQR: 8
IQR: 12
IQR: 15
The following are the test scores of 8 students in Fin Lit: 85, 85, 90, 88, 95, 78, 72, 91. c) Calculate the standard deviation of the data.
Standard deviation: 7.36 (rounded to two decimal places)
Standard deviation: 5.12 (rounded to two decimal places)
Standard deviation: 8.45 (rounded to two decimal places)
Standard deviation: 6.28 (rounded to two decimal places)
The weekly grocery expenses recorded as: 150, 140, 170, 130, 120, 160. a) Find the mean and median of the data.
Mean: 145, Median: 145
Mean: 150, Median: 150
Mean: 140, Median: 140
Mean: 160, Median: 160
The weekly grocery expenses recorded as: 150, 140, 170, 130, 120, 160. b) Compute the inter-quartile range (IQR).
(a)
The weekly grocery expenses recorded as: 150, 140, 170, 130, 120, 160. c) Calculate the standard deviation.
Standard deviation: 18.71 (rounded to two decimal places)
Standard deviation: 15.23 (rounded to two decimal places)
Standard deviation: 20.45 (rounded to two decimal places)
Standard deviation: 12.67 (rounded to two decimal places)
Find A if P = 1800, r = 0.03, n = 4.
A = 2026.45
A = 1950.00
A = 2100.30
A = 1850.75
What is the growth factor in A=2200(1.07)6 ?
Explain why it's helpful to view (1+r)n as a single entity in formulas.
Because it simplifies calculations and makes formulas easier to understand.
Because it increases the value of r.
Because it changes the exponent n.
Because it eliminates the need for parentheses.
If P = 500 and A = 650 after 5 years, what was the growth factor?
Compare simple interest ( A=P(1+rt) ) and compound interest ( A=P(1+r)n ). What’s the key difference?
Simple interest is calculated only on the principal, while compound interest is calculated on principal plus accumulated interest.
Simple interest is calculated on the accumulated interest, while compound interest is only on the principal.
Both are calculated only on the principal.
Both are calculated only on the accumulated interest.
A company sells two products, A and B. The total number of units sold is limited to 500. If the company sells 200 units of A, is selling 350 units of B a viable option?
True
False
A student is budgeting study hours for math and science. They have 10 hours available and plan to spend x hours on math and y hours on science. If they choose x = 6 and y = 4, is this a viable option?
True
False
A factory produces at least 100 units but no more than 500 daily. Can they produce 50 units?
True
False
A parking garage has space for 200 cars. If 180 cars are currently parked, can 30 more enter?
No, because 180 + 30 = 210, which exceeds the maximum capacity of 200.
Yes, because 180 + 30 = 200, which is exactly the maximum capacity.
Yes, because there is always extra space for more cars.
No, because the garage is already full.
A bakery needs to sell at least 300 cupcakes weekly to break even. They sold 280. Was their business viable this week?
No, because 280 < 300, meaning they did not meet the minimum constraint.
Yes, because 280 is close enough to 300, so they likely broke even.
Yes, because selling any amount is viable for the business.
No, because 280 is more than 300, so they did not break even.
A ride at an amusement park requires a height between 48 inches and 80 inches. A person is 45 inches tall. Can they ride?
No, because 45 is less than the minimum height requirement of 48 inches.
Yes, because 45 is within the required height range.
Yes, because 45 is more than the maximum height requirement of 80 inches.
No, because 45 is more than the minimum height requirement of 48 inches.
A shipping company can carry at most 1000 pounds of cargo per trip. If they load 750 pounds and need to add 300 more, is it possible?
No, because 750 + 300 = 1050, which exceeds the 1000-pound limit.
Yes, because 750 + 300 = 950, which is within the limit.
Yes, because 750 + 300 = 1000, which is exactly the limit.
No, because 750 + 300 = 900, which is below the limit.
A classroom has 25 desks. If 20 students are seated, how many more students can sit?
A person must be at least 18 years old to vote. If they are 17 years and 9 months old, can they vote?
No, because they have not yet reached the required minimum age of 18.
Yes, because they are close to 18 years old.
Yes, if they have parental permission.
Yes, if they are registered to vote.
A hotel has 50 rooms available per night. If 47 are booked and a group of 5 requests rooms, can they be accommodated?
No, because only 3 rooms are available, and the group needs 5.
Yes, because the hotel can always make extra space.
Yes, because 5 rooms are always kept for groups.
No, because the hotel is fully booked.
