Question 186441

Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r
Let t=driving time on Wed
Then t+2=driving time on Thu
Total number of hours that he drove on both days=t+t+2=2t+2
Let d=distance that he drove on Wed
then 326-d=distance he drove on Thu and this also equals the distance from Detroit to Hamond, IN.

On Wed:
t=d/47---------------------------eq1
On Thu:
(t+2)=(326-d)/69---------------------eq2
Substitute t=d/47 from eq1 into eq2 and we get:
(d/47) + 2=(326-d)/69 multiply each side by 69*47
69d+6486=47*(326-d)=
69d+6486=15322-47d  add 47d to and subtract 6486 from each side
69d+47d=15322-6486-47d+47d  collect like terms
116d=8836
divide each side by 116
d=76.2 mi-------------------distance drove on Wed
326-d=326-76.2=249.8 mi dist on Thu-----distance from Detroit to Hamond
Substitute d=76.2 into eq1:
t=76.2/47=1.62 hr------driving time on Wed
t+2=1.62+2=3.62 hr------driving time on Thu
Total driving time=1.62 +3.62= 5.24 hr

CK
distance drove on Wed=47*1.62=~~~~76.2
distance drove on Thu=69*3.62=~~~~249.8 mi
76.2+249.8=326
326=326

Hope this helps---ptaylor