Posted: 3/31/2005 1:52:24 PM EDT
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Rational Inequalities Michael trains for a trialthalon. He swims .6 miles, bikes 15 miles, and runs 8 miles. Michael bikes about 9 times as fast as he swims. Michael runs about 6mph faster than he swims. Write a rational function in terms of swimming speed for the total time it takes him to complete his workout. Find the speeds at which he must swim, run and bike to complete his workout in 1.5 hours. Please help my 16 year old has my brain hurting soooo bad. |
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time = distance/velocticy running velocity (rv) running distance (rd) = 8 miles running time (rt) = rd/rv Swimming velocity (sv) Swimming distance (sd) = 0.6 miles Swimming time (st) = sd/sv biking velocity (bv) Biking distance (bd)= 15 miles Biking time (bt) = bd/sv total time (tt)= rt+st+bt tt=rd/rv+sd/sv+bd/bv total time 1.5 hours rv=6+sv bv=9(sv) 1.5(hours)=(8(miles)/(6+sv)) + (.6(miles)/sv) + (15 (miles)/9(sv)) Solve for sv use it to calculate bv and rv |
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Just hammered this out with out checking. I'll leave it to the piranhas to correct any mistakes. Okay, here goes Distance = Rate x Time D=RT ====> T=D/R Ds = swim distance = 0.6m Db = bike distance = 15m Dr = run distance = 8m Rs=swim rate Rb=bike time = 9Rs Rr=run time = Rs+6 Hopefully you're following my subscript scheme: Ts=Ds/Rs, Tb=Db/Rb, Tr=Dr/Rr Ttot = Ts+Tb+Tr = Ds/Rs + Db/9Rs + Dr/(Rs+6) solve for Rs and substitute constants: 13.5Rs^2 -6.6Rs - 93.6 = 0 solve quadratically Rs = 2.89 mph (the other value is negative and so has no physical meaning) So, Rb = 9Rs = 9*2.89 26.01 mph Rr= Rs + 6 = 2.89+6=8.89 mph Everyone, fire for effect... |
The wording is very important
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