Section 2.7 Mixture Applications and Uniform Motion 159 3. Applications Involving Uniform Motion The formula (distance) (rate)(time) or simply, d rt, relates the distance traveled to the rate of travel and the time of travel. For example, if a car travels at 60 mph for 3 hours, then d 160 mph213 hours2 180 miles If a car travels at 60 mph for x hours, then d 160 mph21x hours2 60x miles Solving an Application Involving Distance, Rate, and Time Example 3 One bicyclist rides 4 mph faster than another bicyclist.The faster rider takes 3 hr to complete a race, while the slower rider takes 4 hr.Find the speed for each rider. Solution: Step 1: Read the problem. The problem is asking us to find the speed of each rider. Let x represent the speed of the slower rider. Step 2: Label the variables and organize the information given in the problem.A distance-rate-time chart may be helpful. Then 1x 42 is the speed of the faster rider. Distance Rate Time 31x 42 x 4 3 Faster rider Slower rider 41x2 x 4 To complete the first column, we can use the relationship, d rt . Because the riders are riding in the same race, their distances are equal. Step 3: Write a verbal model. Step 4: Write a mathematical equation. Step 5: Solve the equation. Subtract 3x from both sides. a Distance b by faster rider a by slower rider b 31x 42 41x2 3x 12 4x 12 x distance The variable x represents the slower rider’s rate.The quantity x 4 is the faster rider’s rate.Thus, if x 12, then x 4 16 . The slower rider travels 12 mph and the faster rider travels 16 mph. Skill Practice 3. An express train travels 25 mph faster than a cargo train. It takes the express train 6 hr to travel a route, and it takes 9 hr for the cargo train to travel the same route. Find the speed of each train. Avoiding Mistakes Check that the answer is reasonable. If the slower rider rides at 12 mph for 4 hr, he travels 48 mi. If the faster rider rides at 16 mph for 3 hr, he also travels 48 mi as expected. Answer 3. The express train travels 75 mph, and the cargo train travels 50 mph.
miller_beginning_intermediate_algebra_4e_ch1_3
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