Motion, Money, and Mixture Problems Section 3.4 Motion, Money, and Mixture Problems

Solving Motion Problems Formula: Distance = rate x time (D = rt) Make a table: ITEM RATE x TIME = DISTANCE Item1 Distance 1 Item 2 Distance 2

Fill in the information you know, and set up the variable. Multiply rate by time to get each distance. To write the equation, READ the problem carefully. It could be: Distance 1 – Distance 2 = ___ Distance 1 + Distance 2 = ___ Distance 1 = Distance 2

Examples, from p 211 8) 2 trains in NYC start at the same station going in the same direction on sets of parallel tracks. The local train stops often and averages 18.4 mph. The express train stops less frequently and averages 30.2 mph. In how many hours will the 2 trains by 5.9 miles apart?

16) To get to the top of Whistler Mountain, people must use 2 different ski lifts. The first lift travels 4 mps for 0.2 hours. The 2nd lift travels for 0.3 hours to reach the top of the mountain. If the total distance traveled is 1.2 miles, find the average speed of the 2nd lift.

12) Barb and Sandy are at opposite ends of a shopping mall 4780 12) Barb and Sandy are at opposite ends of a shopping mall 4780.4 feet apart walking towards each other. If Barb walks 1.5 ft per second and Sandy walks 2.2 ft per second, how long will it be before they meet?

Solving Money problems Formula: Interest = Principal x rate x time (in years) (I = PRT) Make a table: Account Principal x Rate x Time = Interest Account 1 Interest 1 Account 2 Interest 2

Examples, p 213 34) Jerry invested $7000, part at 8% simple interest and the rest at 5% simple interest for a period of 1 year. If he received a total annual interest of $476 from both investments, how much did he invest at each rate?

38) Sharon invested $20,000, part at 5% and part at 7% simple interest for a period of 1 year. How much was invested in each account if the interest earned in the 7% account was $440 greater than the interest earned in the 5% account?

Mixture Problems Quantity x Price (or %) = Amount Set up another table! Amount 1 + Amount 2 = Amount Mixture Quantity x Price per unit or strength % = Amount Item 1 Amount of 1 Item 2 Amount of 2 Mixture Amount of mix

Examples from p 213 48) Scott’s © Family grass seed sells for $2.45 per lb and Scott’s Spot Filler grass seed sells for $2.10 per lb. How many lbs of each should be mixed to get a 10 lb mixture that sells for $2.20 per lb?

50) At Agway Gardens, bird food is sold in bulk 50) At Agway Gardens, bird food is sold in bulk. In one barrel are sunflower seeds that sell for $1.80 per lb. In a second barrel is cracked corn that sells for $1.40 per lb. If a mixture is made by taking 2.5 lbs of sunflower seeds and 1 lb of cracked corn, what should the mixture per lb cost?

From p 214 54) Susan, a pharmacist, has a 60% solution of sodium iodite. She also has a 25% solution of the same drug. She gets a prescription calling for a 40% solution of the drug. How much of each solution should she mix to make 0.5 liter of the 40% solution?

Also from p 214 66) Miracle-Gro © All Purpose liquid plant food has 12% nitrogen. Miracle-Gro Quick Start liquid plant food has 4% nitrogen. If 2 cups of the All Purpose plant food are mixed with 3 cups of the Quick Start plant food, determine the percent of nitrogen in the mixture.