Training Colts — Math Worksheet for 13-Year-Olds (Middle School): Ratios, Rates & Word Problems

Instructions

Welcome, young trainer! It's time to apply your math skills to the world of training colts. Read each problem carefully and show your work on a separate piece of paper to solve these common equestrian challenges. Round your final answers to the nearest hundredth where necessary.

Paddock Problems

1. Feed Ratios: A growing colt needs a specific feed mix. The ideal ratio of hay to grain by weight is 7:2. If you feed the colt 21 pounds of hay each day, how many pounds of grain should it receive?

2. Training Progress: In the first week of training, a colt can hold a trot for an average of 90 seconds. After a month of consistent work, the colt can now hold a trot for an average of 120 seconds. What is the percentage increase in the colt's trotting time?

3. The Round Pen: You are building a circular round pen for groundwork. You decide the diameter should be 50 feet.
   a) How many feet of fencing will you need to enclose the pen? (Use π ≈ 3.14)
   b) What is the total training area inside the pen in square feet? (Use π ≈ 3.14)

4. Paddock Pace: A colt is turned out in a rectangular paddock that is 100 feet long and 80 feet wide. If the colt canters the entire perimeter of the paddock in 30 seconds, what is its speed in feet per second?

5. Scheduling Sessions: A training session is 60 minutes long. The time spent on groundwork (g) is twice the time spent on lunging (l). The entire session is spent on only these two activities. Write and solve an equation to find out how many minutes are spent on groundwork and how many are spent on lunging.

6. Vet Visit Costs: The veterinarian's bill for a colt's check-up is $180. Your training stable gets a 15% discount for being a regular client. However, you must add a 5% service fee to the discounted price. What is the final amount you have to pay?

Answer Key

1. 6 pounds of grain.
   Explanation: The ratio is 7:2. Set up a proportion: 7/2 = 21/x. Cross-multiply to get 7x = 42. Solve for x: x = 6.

2. 33.33% increase.
   Explanation: First, find the amount of increase: 120 - 90 = 30 seconds. Then, calculate the percentage increase: (Increase / Original Amount) × 100. So, (30 / 90) × 100 ≈ 33.33%.

3. a) 157 feet of fencing.
   Explanation: The formula for the circumference of a circle is C = πd. C = 3.14 × 50 = 157 feet.
   b) 1,962.5 square feet.
   Explanation: The formula for the area of a circle is A = πr². First, find the radius (diameter / 2), which is 50 / 2 = 25 feet. Then, A = 3.14 × (25)² = 3.14 × 625 = 1962.5 sq ft.

4. 12 feet per second.
   Explanation: First, find the perimeter of the paddock: P = 2(length + width) = 2(100 + 80) = 360 feet. Speed is distance divided by time. Speed = 360 feet / 30 seconds = 12 ft/s.

5. 40 minutes on groundwork and 20 minutes on lunging.
   Explanation: Set up the equations: g + l = 60 and g = 2l. Substitute the second equation into the first: 2l + l = 60. This simplifies to 3l = 60. Solve for l: l = 20 minutes. Then find g: g = 2 × 20 = 40 minutes.

6. $160.65
   Explanation: First, calculate the discount: $180 × 0.15 = $27. Subtract the discount from the original price: $180 - $27 = $153. Then, calculate the service fee on the discounted price: $153 × 0.05 = $7.65. Add the fee to the discounted price: $153 + $7.65 = $160.65.