Question 186441: Ali plans a road trip from Chicago to Detroit in his Honda Accord with an overnight stay in Hammond, Indiana. On Wednesday, he drove from Chicago to Hamond at an average speed of 47 mph. On Thursday, he continued to drive from Hamond to Detroit at an average speed of 69 mph. His driving time on Thursday is 2 hours longer that his driving time on Wednesday. If the total distance from Chicago to Detroit is 326 miles, then what is the total number of hours he drove on both days? How far is Detroit from Hamond, IN?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
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
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