SOLUTION: Two cars leave town at the same time going in the same direction on the same road. One travels 30 mi/h and the other travels 46 mi/h. In how many hours will they be 72 miles apart?

Algebra ->  Expressions-with-variables -> SOLUTION: Two cars leave town at the same time going in the same direction on the same road. One travels 30 mi/h and the other travels 46 mi/h. In how many hours will they be 72 miles apart?      Log On


   



Question 187393This question is from textbook Algebra 1
: Two cars leave town at the same time going in the same direction on the same road. One travels 30 mi/h and the other travels 46 mi/h. In how many hours will they be 72 miles apart? This question is from textbook Algebra 1

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For the 30 mi/hr car:
(1) d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
For the 46 mi/hr car:
(2) d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
given:
t%5B1%5D+=+t%5B2%5D
r%5B1%5D+=+30
r%5B2%5D+=+46
------------------
d%5B2%5D+=+d%5B1%5D+%2B+72
The faster car goes 72 mi further than the slower car
I can rewrite (1) and (2)
(1) d%5B1%5D+=+30t%5B1%5D
(2) d%5B1%5D+%2B+72+=+46t%5B1%5D
(2) d%5B1%5D+=+46t%5B1%5D+-+72
Note that t%5B1%5D+=+t%5B2%5D since they travel different
distances but in the same amount of time
Since both left sides are d%5B1%5D, I can set the
right sides equal to eachother
30t%5B1%5D+=+46t%5B1%5D+-+72
16t%5B1%5D+=+72
t%5B1%5D+=+4.5 hr
and
t%5B2%5D+=+4.5 hr also
In 4.5 hrs they will be 72 mi apart
Now check the answer:
(1) d%5B1%5D+=+30t%5B1%5D
(1) d%5B1%5D+=+30%2A4.5
(1) d%5B1%5D+=+135 mi
and
(2) d%5B1%5D+%2B+72+=+46t%5B1%5D
(2) 135+%2B+72+=+46%2A4.5
(2) 207+=+207
OK