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Word Problem: Rational Expressions? |
Really lost please help! I want to understand how to do this! Bob and Jack enter a 1000-km bicycle race. Bob cycles 4 km/h faster than Jack, but his bicycle gets a flat tire, which takes 30 minutes to repair. If the both of them finish the race in a tie, then how fast was each boy cycling? Give your answer in one decimal place. Use the relation distance = rate*time. d=rt Call Bob's rate while moving b and the time that he's moving t. Bob also has a rate of 0 km/h for 30 min = .5h. 1000 = b*t + 0*(.5) 1000 = b*t Jack's rate (call it j) is 4 km/h less than Bob's. The amount of time he's moving (call it u) is .5 hours more. j = b-4 u = t + .5 1000 = j*u 1000 = (b-4)*(t + .5) Now there are two equations and two unknown variables. 1000 = bt => t = 1000/b 1000 = (b-4)*(t + .5) = (b-4)(1000/b + .5) = 1000 + .5b - 4000/b - 2 Canceling the 1000s and multiplying both sides by 2b gives 0 = b^2 - 4b - 8000 With the quadratic formula, b = [4 +/- sqrt( (-4)^2 - 4*1*(-8000) )] / (2*1) = 91.5 or -87.5 km/h Use the positive rate. Then Bob's rate is b = 91.5 km/h and Jack's is j = b - 4 = 87.5 km/h |
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