Two runners are training for their next competitions. Each runner is able to run a certain...

 

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Two runners are training for their next competitions. Each runner is able to run a certain distance in proportion to the time. The table on the left displays the distance Runner A can run in relation to the time. Meanwhile, the graph on the right displays the distance Runner B can run in relation to time. Runner A Time (in seconds) Distance (in feet) 4.5 54 13 156 22.5 270 Distance (in feet) 325 300 275 250 225 200 175 150 125 100 75 50 25 0 Runner B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time (in seconds) What are the unit rates for the two runners? Which runner can run faster? 2. There are two submarines, Submarine 1 and Submarine 2, that are diving under the sea. The proportional equation y = -22x represents the relationship between the depth below sea level (in feet) of Submarine 1 to the time (in minutes). Meanwhile, the graph shown here represents the relationship between the depth below sea level (in feet) and the time (in minutes) of Submarine 2: Submarine 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 sids A 19 0 0 1 1 2 0 -20 -40 -60 -80 -100 -120 Depth Below Sea Level (in feet) -140 -160 -180 @-200 -220 -240 -260 -280 -300 -320 -340 -360 -380 -400 -420 -440 -460 -480 -500 Time (in minutes) Determine which submarine will reach a depth of -1,056 feet below sea level in the fastest time. How long will it take the faster submarine to reach a depth of -1,056 feet below sea level? 4. Jess is playing the newest video game. The object of the game is to collect as many points as you can in the shortest time. The amount of points Jess collects is directly proportional to the number of hours she plays. This relationship is represented in the graph shown here: Points Collected Jess's Points Collected in Relation to the Time (hrs.) 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0 1 2 3 4 5 67 7 8 9 10 Time (in hours) Meanwhile, her friend Kira has also been playing the game. At the end of each day, she recorded the number of points she collected. It turns out, she is collecting points in direct proportion to the number of days she plays. This relationship is represented by the equation: y = 440x. Who is collecting points faster in this new game, Jess or Kira? 3. At the local grocery store (Store A), the price of carrots is proportional to their weight, in ounces. The equation representing this relationship is given by y = 0.40x. Meanwhile, the market in the next town (Store B) sells their carrots by the pound, represented in the table shown here: Store B Carrots (in pounds) Price ($) 3 20.16 5 33.60 9 60.48 Which store is currently selling their carrots at a cheaper unit rate? Two runners are training for their next competitions. Each runner is able to run a certain distance in proportion to the time. The table on the left displays the distance Runner A can run in relation to the time. Meanwhile, the graph on the right displays the distance Runner B can run in relation to time. Runner A Time (in seconds) Distance (in feet) 4.5 54 13 156 22.5 270 Distance (in feet) 325 300 275 250 225 200 175 150 125 100 75 50 25 0 Runner B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time (in seconds) What are the unit rates for the two runners? Which runner can run faster? 2. There are two submarines, Submarine 1 and Submarine 2, that are diving under the sea. The proportional equation y = -22x represents the relationship between the depth below sea level (in feet) of Submarine 1 to the time (in minutes). Meanwhile, the graph shown here represents the relationship between the depth below sea level (in feet) and the time (in minutes) of Submarine 2: Submarine 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 sids A 19 0 0 1 1 2 0 -20 -40 -60 -80 -100 -120 Depth Below Sea Level (in feet) -140 -160 -180 @-200 -220 -240 -260 -280 -300 -320 -340 -360 -380 -400 -420 -440 -460 -480 -500 Time (in minutes) Determine which submarine will reach a depth of -1,056 feet below sea level in the fastest time. How long will it take the faster submarine to reach a depth of -1,056 feet below sea level? 4. Jess is playing the newest video game. The object of the game is to collect as many points as you can in the shortest time. The amount of points Jess collects is directly proportional to the number of hours she plays. This relationship is represented in the graph shown here: Points Collected Jess's Points Collected in Relation to the Time (hrs.) 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0 1 2 3 4 5 67 7 8 9 10 Time (in hours) Meanwhile, her friend Kira has also been playing the game. At the end of each day, she recorded the number of points she collected. It turns out, she is collecting points in direct proportion to the number of days she plays. This relationship is represented by the equation: y = 440x. Who is collecting points faster in this new game, Jess or Kira? 3. At the local grocery store (Store A), the price of carrots is proportional to their weight, in ounces. The equation representing this relationship is given by y = 0.40x. Meanwhile, the market in the next town (Store B) sells their carrots by the pound, represented in the table shown here: Store B Carrots (in pounds) Price ($) 3 20.16 5 33.60 9 60.48 Which store is currently selling their carrots at a cheaper unit rate?