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5 question math prob!!! NEED HELP!!!? |
Years after the famous foot race, the hare challenged the tortoise to a rematch on bicycles. The hare was able to pedal at a rate of 15 miles per hour (mph), while the tortoise could pedal only at a rate of 12mph. Knowing he was slower, the tortoise makes up a lame excuse for being given a 27-mile head start in the 165-mile race. 1.Who won the tortoise and the hare race? By how much time? Explain. 2.How far into the race did the hare overtake the tortoise? 3.What is the largest head start the tortoise could have been given without being able to beat the hare? 4.Despite their size, chipmunks are fast on bikes. Suppose a chipmunk entered the race with an 84-mile head start and traveled at a rate of 9mph. 5.A confused pig also followed the race course. The pig started at the finish line at a rate of 15 mph and rode his bike backwards. Where and when did he meet the hare on the road? Explain everything and why you chose that step. Speed x time = distance 15H = 165 divide both sides by 15 and you get: H = 11 hours for the hare to finish from mile 0 to 165 12T = 165 - 27 (since the turtle gets a 27 mile head start) 12T = 138 divide both sides by 12 T = 11.5 from mile 27 to mile 165 (this is from the time the hare leaves, and not the total time the turtle has been travelling) 11.5-11 = .5 hours (30 minutes) The turtle will finish a half hour after the hare finishes. Now you want to set the distances equal to each other and find the time when they meet. First, find the time when the turtle reaches the 27 mile mark 12T = 27 T = 2.25 (2 hours and 15 minutes after the turtle starts he will reach mile 27) Put T-2.25 with the speed of the hare to hold him back until the turtle is at mile 27 - the hare's time "0" (starting time) won't be until 2.25 hours has passed. Since the distances from the start are equal, set them equal to each other and solve. 15(T-2.25) = 12T make sure you distribute the 15 15T - 33.75 = 12T subtract 12T and add 33.75 to both 3T = 33.75 divide by 3 on both sides T = 11.25 11 hours and 15 minutes after the tortoise starts is when the hare will catch him. The hare will only have been biking for 9 hours (11.25 - 2.25) The total time for the tortoise is 13.75 hours The total time for the hare is 11 hours 13.75 - 11 = 2.75 any lead greater than 2.75 hours will cause the tortoise to win. In distance that is: 12*2.75 = 33 miles Over a 33 mile lead and the tortoise wins. 9S = 165 - 84 9S = 81 S = 9 hours after the tortoise starts (if they mean the next competitor has to wait until the squirrel gets to mile 84) so the squirrel would beat the tortoise and the hare both to the finish line Total time for squirrel 18 hours and 20 minutes (84/9 + 9) Total time for tortoise 13 hours 45 minutes (2.25 + 11.5) Total time for hare 11 hours 15H = 165-x (hare needs to travel the ditance the pig doesn't cover) 15H = x (distance pig travels in time H) 15H = 165 - 15H 30H = 165 H = 5.5 hours This makes sense since effectively the hare is travelling twice as fast if the "finish line" (the pig) is moving toward him at the same speed. WOAH!!! Seriously, you probably aren't getting any answers because no one wants to take the time to figure that out. You need to break it up!! It is part of the whole asking a question process. Think about it: There are a lot of questions out there, and you need to be able to come up with a way to word it so people will want to answer it. WORK ON IT Do your own homework! Hare = 15 mph = 11 hours Tortoise = 12 mph = 11.5 hours Total Miles : 165-miles Tortoise= 27 mile head starts... 138 miles left The tortoise had a 27-mile headstart; therefore, you take 165 miles - 27 miles = 138 miles, then you divide 138 by 27, which gives you 11 hours. Then, you take 165 total miles divided by 15 mph for the Hare--which gives you 11.5 hours--which is equal to 11 1/2 hours. So; therefore, the Hare ended up winning. |
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