180 Chapter 2 Linear Equations and Inequalities Concept 3: Applications Involving Uniform Motion 29. a. If a car travels 60 mph for 5 hr, find the distance traveled. 300 mi b. If a car travels at x miles per hour for 5 hr, write an expression that represents the distance traveled. 5x c. If a car travels at x 12 mph for 5 hr, write an expression that represents the distance traveled. 51x 122 or 5x 60 30. a. If a plane travels 550 mph for 2.5 hr, find the distance traveled. 1375 mi b. If a plane travels at x miles per hour for 2.5 hr, write an expression that represents the distance traveled. 2.5x c. If a plane travels at x 100 mph for 2.5 hr, write an expression that represents the distance traveled. 2.51x 1002 or 2.5x 250 25. A pharmacist needs to mix a 1% saline (salt) solution with 24 milliliters (mL) of a 16% saline solution to obtain a 9% saline solution. How many milliliters of the 1% solution must she use? 26. A landscaper needs to mix a 75% pesticide solution with 30 gal of a 25% pesticide solution to obtain a 60% pesticide solution. How many gallons of the 75% solution must he use? The landscaper needs to use 70 gal of the 75% pesticide solution. 27. To clean a concrete driveway, a contractor needs a solution that is 30% acid. How many ounces of a 50% acid solution must be mixed with 15 oz of a 21% solution to obtain a 30% acid solution? The contractor needs to mix 6.75 oz of 50% acid solution. 28. A veterinarian needs a mixture that contains 12% of a certain medication to treat an injured bird. How many milliliters of a 16% solution should be mixed with 6 mL of a 7% solution to obtain a solution that is 12% medication? The veterinarian needs to use 7.5 mL of the 16% solution. The pharmacist needs to use 21 mL of the 1% saline solution. Distance Rate Time Downhill to the lake Uphill from the lake 33. Bryan hiked up to the top of City Creek in 3 hr and then returned down the canyon to the trailhead in another 2 hr. His speed downhill was 1 mph faster than his speed uphill. How far up the canyon did he hike? Bryan hiked 6 mi up the canyon. 34. Laura hiked up Lamb’s Canyon in 2 hr and then ran back down in 1 hr. Her speed running downhill was 2.5 mph greater than her speed hiking uphill. How far up the canyon did she hike? Laura hiked 5 mi up the canyon. 31. A woman can walk 2 mph faster down a trail to Cochita Lake than she can on the return trip uphill. It takes her 2 hr to get to the lake and 4 hr to return.What is her speed walking down to the lake? (See Example 3.) She walks 4 mph to the lake. 32. A car travels 20 mph slower in a bad rain storm than in sunny weather. The car travels the same distance in 2 hr in sunny weather as it does in 3 hr in rainy weather. Find the speed of the car in sunny weather. The car travels 60 mph in sunny weather. Distance Rate Time Rain storm Sunny weather 35. Hazel and Emilie fly from Atlanta to San Diego. The flight from Atlanta to San Diego is against the wind and takes 4 hr. The return flight with the wind takes 3.5 hr. If the wind speed is 40 mph, find the speed of the plane in still air. The plane travels 600 mph in still air. 36. A boat on the Potomac River travels the same 23 distance downstream in hr as it does going upstream in 1 hr. If the speed of the current is 3 mph, find the speed of the boat in still water. The speed of the boat is 15 mph in still water. 37. Two cars are 200 mi apart and traveling toward each other on the same road. They meet in 2 hr. One car is traveling 4 mph faster than the other.What is the speed of each car? (See Example 4.) The slower car travels 48 mph and the faster car travels 52 mph. 38. Two cars are 238 mi apart and traveling toward each other along the same road. They meet in 2 hr. One car is traveling 5 mph slower than the other.What is the speed of each car? The cars are traveling 62 mph and 57 mph. Writing Translating Expression Geometry Scientific Calculator Video
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