Question

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)

Answer 1

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

Answer 2

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