Solving Work Problems and Distance Problems Rational Equation

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

• 48 minutes

• 50 minutes

• 24 minutes

• 12 minutes

Which of the following equations makes the most sense for the following situation: Jerry works twice as fast as Kenny. If Jerry works for 2 hours and is then joined by Kenny...and they work an additional 3 hours...how fast could they each do the job alone?

One crew can sow a field of corn in 6 days. A different crew can do the same job in 3 days. If the slow crew works alone for 2 days and then is joined by the faster crew, how long will it take them to finish?

• not enough information to tell

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she spends $35 in all.

• .50x + 20 = 35

• .50x = 35

• .50 + 20x = 35 

• .50x - 20 = 35

WRITE AN EQUATION
Aliyah had some candy to give to her four children. She first took ten pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?

• (x-10)/4=2

• x-10/4=2

• x-10=2(4)

• 2(x-10)=4

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

• 150x + 24 = 180 + 20x

• 150 + 24x = 180 + 20x

• 180 - 150 = 24 x + 20x

• 150 - 24x = 180 - 20x

Tank 1 currently has 40 gallons of water and is filling at a rate of 1.5 gallons per minute. Tank 2 has 220 gallons of water and is draining at a rate of 3 gallons per minute. After how many minutes will the two tanks have the same amount of water? Write the equation.

You are hosting a bake sale, but it isn't going well! You decide to reduce your prices by $0.75, and then you get 15 sales for a total of $33.75. What was your original price per item? Write the equation.

• 15p-0.75=33.75

• 15(p-0.75)=33.75

• 0.75p+15=33.75

• 33.75-0.75p=15

You and your friend are participating in the hot air balloon festival! Your balloon is currently 200 feet in the air, and descending at a rate of 3ft per sec. Your friend is 75 feet in the air, an ascending at a rate of 2ft per sec. After how many seconds will you both be at the same height? Write the equation.

• 200+3x=75-2x

• 200-3x=75+2x

• 200-3x=75-2x

• 200+3x=75+2x

Maria has 25 dollars. She has to buy a gallon of milk which costs $3.50. She wants to spend the rest of her money on cereal. If each box of cereal costs $4.50, how many can she purchase? Write the equation.

• 3.50+4.50x=25

• 3.50x+4.50=25

• 25-3.50x=4.50

• 4.50x-3.50=25