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Example 1 Understanding and Planning The table shows the biking and running speeds (in meters per minute) for both you and your friend. Who has the better total time? DUATHLON You and a friend decide to compete in a duathlon. You both bike 10, 000 meters and run 4000 meters. To solve this problem, you need to make sure you understand the problem. Then make a plan for solving the problem.
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Example 1 Understanding and Planning READ AND UNDERSTAND What do you know? The table displays the speeds of you and your friend for biking and running. You both bike 10,000 meters and run 4000 meters. What do you want to find out? Who has the better total time for biking and running?
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Example 1 Understanding and Planning MAKE A PLAN How can you relate what you know to what you want to find out? Find each of your biking and running times. You can organize this information in a table. Find each of your total times and then compare these times. You will solve the problem in Example 2.
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Example 2 Solving and Looking Back DUATHLON Carry out the plan from Example 1 to solve the problem. Then, check your answer. SOLVE THE PROBLEM Use the formula Time. = Rate Distance
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Example 2 Solving and Looking Back BikingRunning Friend You = t r d = 410 10, 000 ≈24.4 min = t r d = 430 10, 000 ≈23.3 min = t r d = 170 4000 ≈23.5 min = t r d = 160 4000 ≈25 min
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Example 2 Solving and Looking Back Add to find the total times. 47.9 min = 23.5+24.4 You Friend 48.3 min = 25+23.3 You have the better total time for the duathlon. ANSWER
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Example 2 Solving and Looking Back LOOK BACK Does your answer make sense? You bike more slowly than your friend, so your biking time should be greater. You run faster than your friend, so your running time should be less. Therefore, the calculations are reasonable.
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Guided Practice for Examples 1 and 2 1. ANSWER 22.7 min ; your friend WHAT IF? In Examples 1 and 2, suppose that your friend bikes at a rate of 440 meters per minute. What is your friend’s biking time? Who has the better total time in the duathlon?
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