Connor and Matt walk a 12 mile couse as part of a fitness program. Matt walks 1 mi/hr faster than Connor, and it takes him 1 hour less than Connor to complete the course. How long does it take Connor to complete the course? (work too please) (fyi answer is 5 hours)

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Connor and Matt walk a 12 mile couse as part of a fitness program. Matt walks 1 mi/hr faster than Connor, and it takes him 1 hour less than Connor to complete the course. How long does it take Connor to complete the course? (work too please) (fyi answer is 5 hours)

Mathematics
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d = r*t for both Matt and Connor, d = 12 Let r be Connors speed and t be his time Then Matts speed is r+1 because he walks 1 mph faster Matts time is t-1 because it takes 1 less hour to complete course set up system of 2 equations: (i) r*t = 12 (ii) (r+1)(t-1) = 12 expand (ii) r*t -r +t -1 = 12 replace r*t with 12 from (i) 12 -r +t -1 =12 solve for r -r + t = 1 r = t-1 replace r with t-1 in (i) t*(t-1) = 12 t^2 -t -12 = 0 (t-4)(t+3) =0 t must be positive for this problem (cant walk 12mi in neg time) t = 4 therefore r = 3 It takes Conner 4 hours to walk 12mi at rate of 3 mph
not sure where you got 5 from if t=5 then r = d/t = 12/5 = 2.4 matt rate would be 3.4 his time would be d/r = 12/3.4 = 3.52 this is more than an hour faster than Conner

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