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Section 2.7 Mixture Applications and Uniform Motion 181 39. After Hurricane Katrina, a rescue vehicle leaves a station at noon and heads for New Orleans. An hour later a second vehicle traveling 10 mph faster leaves the same station. By 4:00 P.M., the first vehicle reaches its destination, and the second is still 10 mi away. How fast is each vehicle? The speeds of the vehicles are 40 mph and 50 mph. 40. A truck leaves a truck stop at 9:00 A.M. and travels toward Sturgis,Wyoming. At 10:00 A.M., a motorcycle leaves the same truck stop and travels the same route. The motorcycle travels 15 mph faster than the truck. By noon, the truck has traveled 20 mi farther than the motorcycle. How fast is each vehicle? The speed of the motorcycle is 65 mph and the speed of the truck is 50 mph. 41. In the Disney Marathon, Jeanette’s speed running was twice Sarah’s speed walking. After 2 hr, Jeanette was 7 mi ahead of Sarah. Find Jeanette’s speed and Sarah’s speed. Sarah walks 3.5 mph and Jeanette runs 7 mph. 42. Two canoes travel down a river, starting at 9:00 A.M. One canoe travels twice as fast as the other. After 3.5 hr, the canoes are 5.25 mi apart. Find the speed of each canoe. The canoes travel 1.5 mph and 3 mph. 43. A certain granola mixture is 10% peanuts. a. If a container has 20 lb of granola, how many pounds of peanuts are there? 2 lb b. If a container has x pounds of granola, write an expression that represents the number of pounds of peanuts in the granola. 0.10x c. If a container has x 3 lb of granola, write an expression that represents the number of pounds of peanuts. 0.101x 32 0.10x 0.30 44. A certain blend of coffee sells for $9.00 per pound. a. If a container has 20 lb of coffee, how much will it cost. $180 b. If a container has x lb of coffee, write an expression that represents the cost. 9.00x c. If a container has 40 x lb of this coffee, write an expression that represents the cost. 9140 x2 360 9x Mixed Exercises 45. The Coffee Company mixes coffee worth $12 per pound with coffee worth $8 per pound to produce 50 lb of coffee worth $8.80 per pound. How many pounds of the $12 coffee and how many pounds of the $8 coffee must be used? 10 lb of coffee sold at $12 per pound and 40 lb of coffee sold at $8 per pound $12 Coffee $8 Coffee Total Number of pounds Value of coffee 46. The Nut House sells pecans worth $4 per pound and cashews worth $6 per pound. How many pounds of pecans and how many pounds of cashews must be mixed to form 16 lb of a nut mixture worth $4.50 per pound? 12 lb of pecans and 4 lb of cashews $4 Pecans $6 Cashews Total Number of pounds Value of nuts 47. A boat in distress, 21 nautical miles from a marina, travels toward the marina at 3 knots (nautical miles per hour). A coast guard cruiser leaves the marina and travels toward the boat at 25 knots. How long will it take for the boats to reach each other? The boats will meet in hr (45 min). 34 48. An air traffic controller observes a plane heading from New York to San Francisco traveling at 450 mph. At the same time, another plane leaves San Francisco and travels 500 mph to New York. If the distance between the airports is 2850 mi, how long will it take for the planes to pass each other? The planes will pass in 3 hr. 49. Surfer Sam purchased a total of 21 items at the surf shop. He bought wax for $3.00 per package and sunscreen for $8.00 per bottle. He spent a total amount of $88.00. How many of each item did he purchase? Sam purchased 16 packages of wax and 5 bottles of sunscreen. 50. Tonya Toast loves jam. She purchased 30 jars of gourmet jam for $178.50. She bought raspberry jam for $6.25 per jar and strawberry jam for $5.50 per jar. How many jars of each did she purchase? Tonya purchased 18 jars of raspberry and 12 jars of strawberry. Writing     Translating Expression     Geometry      Scientific Calculator     Video


miller_introductory_algebra_3e_ch1_3
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