You Friend EXAMPLE 1 Understanding and Planning

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Presentation transcript:

You Friend EXAMPLE 1 Understanding and Planning You and a friend decide to compete in a triathlon. You both swim 200 meters, bike 10 kilometers, and then run 2 kilometers. The table shows your speeds for swimming in meters per minute, and biking in kilometers per minute. Who has the better total time after these two stages? Swimming (m/min) Biking (km/min) You 76.9 0.43 Friend 82.6 0.41

EXAMPLE 1 Understanding and Planning To solve the triathlon problem, you need to make sure you understand the problem. Then make a plan for solving the problem. READ AND UNDERSTAND What do you know? The table displays your speeds for each stage. You both swim 200 meters and bike 10 kilometers. What do you want to find out? Who has the better total time for swimming and biking?

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 swimming and biking 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.

GUIDED PRACTICE for Example 1 1. Which formula would you use to find swimming and running times? Explain your reasoning. distance rate time = A. distance = rate time B. distance time rate = C. ANSWER B; You need to use the formula to find time.

EXAMPLE 2 Solving and Looking Back Carry out the plan from Example 1. Check the answer. SOLVE THE PROBLEM distance rate Use the formula time = .

EXAMPLE 2 Solving and Looking Back Add to find the total time. You 2.60 + 23.26 = 25.86 min Friend 2.42 + 24.39 = 26.81 min You have the better total time after the two stages. ANSWER

GUIDED PRACTICE for Example 2 2. What If? Suppose in Example 2 that your friend biked at a rate of 0.44 km/min. Who had the better total time after two stages? Your friend has a better total time after the two stages. ANSWER

EXAMPLE 3 Using a Problem Solving Plan City Blocks In parts of New York City, the blocks between avenues are called long blocks. There are 4 long blocks per mile. Blocks between streets are called short blocks. There are 20 short blocks per mile. You walk 40 short blocks and 6 long blocks. How many miles do you walk?

EXAMPLE 3 Using a Problem Solving Plan SOLUTION Read and Understand You walk 40 short blocks and 6 long blocks. There are 20 short blocks per mile and 4 long blocks per mile. You are asked to find how many miles you walk. Make a Plan Convert short blocks to miles and long blocks to miles using unit analysis. Then add to find the total miles. 1 mile 20 short blocks Solve the Problem Because 20 short blocks equal one mile, you can multiply the number of short blocks by to convert to miles.

EXAMPLE 3 Using a Problem Solving Plan 40 short blocks 1 mile 20 short blocks = 2 miles You can convert long blocks to miles by multiplying by 1 mile 4 long blocks . 6 long blocks = 1.5 miles 1 mile 4 long blocks You walk a total of 2 + 1.5 = 3.5 miles. ANSWER

GUIDED PRACTICE for Example 3 3. What If? In Example 3, how many miles do you walk if you walk 50 short blocks and 12 long blocks? 50 short blocks = 2.5 miles 1 mile 20 short blocks You can convert long blocks to miles by multiplying by 1 mile 4 long blocks . 12 long blocks = 3 miles 1 mile 4long blocks You walk a total of 2.5 + 3 = 5.5 miles. ANSWER