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Motion, Money, and Mixture Problems: Section 3.4

This section covers motion problems, distance problems, problems with two rates, money problems, and mixture problems. Learn how to solve various mathematical problems involving rates, time, distance, and money.

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Motion, Money, and Mixture Problems: Section 3.4

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  1. Motion, Money and Mixture Problems Section 3.4

  2. Motion Problems amount = rate · time A motion problemis one in which an object is moving at a specified rate for a specified period of time. Example: A typical shower uses 30 gallons of water and lasts for 6 minutes. How much water is typically used per minute? Continued.

  3. Distance Problems When the amount in the formula is distance, we refer to the formula as the distance formula. distance = rate · time or d = r · t Example: While swimming in the ocean, Elyse’s glasses fell off her head. If the glasses fall at a rate of 4 feet per second, how long will it take for them to fall 70 feet to the sand at the bottom? Continued.

  4. Problems with Two Rates Example: Two crews are laying blacktop on a road. They start at the same time at opposite ends of a 12-mile road and work toward one another. One crew lays blacktop at an average rate of 0.75 mile a day faster than the other crew. If the two crews meet after 3.2 days, find the rate of each crew. Continued.

  5. Problems with Two Rates Example: Kelsey started driving to the mall at an average speed of 30 mile per hour. A short while later, she realized she forgot her wallet. She turned around and headed back to the house, driving 20 miles per hour. If it took her a total of 0.6 hours for the round trip, how far had she driven before she turned around? Continued.

  6. Money Problems interest = principal · rate · time Example: Jordan invested $12,500, part at 7% simple interest and part at 6% simple interest for 1 year. How much was invested at each rate if each account earned the same interest? Continued.

  7. Mixture Problems Any problem in which two or more quantities are combined to produce a different quantity may be considered a mixture problem. strength · quantity = amount

  8. Mixture Problems Example: At a local pet store, bird food is sold in bulk. In one barrel are sunflower seeds that sell for $1.80 per pound. In another barrel is cracked corn that sells for $1.40 per pound. If the store makes bags of a mixture of the two by mixing 2.5 pounds of sunflower seeds with 1 pound of the cracked corn, what should be the cost per pound? Continued.

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