# SOLUTION: Hi can you help me work the following problem? The elevator in the Washington Monument takes 75 seconds to travel 500 ft. to the top floor. What is the speed of the elevator in

Algebra ->  -> SOLUTION: Hi can you help me work the following problem? The elevator in the Washington Monument takes 75 seconds to travel 500 ft. to the top floor. What is the speed of the elevator in       Log On

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 Click here to see ALL problems on Expressions-with-variables Question 95516: Hi can you help me work the following problem? The elevator in the Washington Monument takes 75 seconds to travel 500 ft. to the top floor. What is the speed of the elevator in miles per hours? Give your answers to two significant digits. Thanks. Found 2 solutions by bucky, stanbon:Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!You are given that the elevator in the Washington Monument goes up at a speed of 500 feet in 75 seconds. You can write 500 feet per 75 seconds in this form: . . To convert this to miles/hour you need a couple of conversion factors. . First you need to know that the quantity 5280 feet is equal to 1 mile . Then you need to know that 60 sec is equivalent to 1 minute . Finally you need to know that 60 minutes is equal to 1 hour . You use these conversion factors to multiply the original problem you were given and this will convert that given to miles/hour. . The trick is to recognize that you want to cancel the feet out and replace it with miles. Notice that the units of feet are in the numerator. Therefore, you need the conversion factor to have feet in the denominator. So the conversion factor we will use is: . . And we will multiply that times . Next, we need to get rid of the seconds in the denominator of the original given problem. To do that we need to have seconds in the numerator. That means that we need to have our first conversion of time be in the form . That will get rid of the secs but will leave you with min in the denominator. To get rid of the min in the denominator we need to have units of min in the numerator. So our next conversion factor is: . . . Now we are ready to multiply the original given by the three conversion factors. In algebraic form this becomes: . . Notice the pattern of how the units cancel: . . Notice that the only units that are left are miles in the numerator and hrs in the denominator. Therefore, all we have to do is multiply the numbers in the numerator and divide by the numbers in the denominator and we will have the answer in miles per hour. . The multiplication of the numbers is: . . So the answer is 4.54545454 miles per hour and you can round this off to the two significant digits as required by the problem. . Hope this shows you a logical approach to making the conversion factors work for you. By ensuring that the units cancel to leave you with the units you need for the answer you will be helping to make sure the conversion factors are not accidentally inverted so that you don't build in a multiplication mistake. Answer by stanbon(60772)   (Show Source): You can put this solution on YOUR website!The elevator in the Washington Monument takes 75 seconds to travel 500 ft. to the top floor. What is the speed of the elevator in miles per hours? Give your answers to two significant -------------------- 500 ft/75 seconds (3600 seconds/1 hr.)(1 mi/5280 ft) Notice that the feet cancel and the seconds cancel leaving you with: = [500*3600*1]/[75*1*5280] (mi/hr) = [1800000]/[395000] mi/hr = 4.55 mi/hr ============ Cheers, Stan H.