SOLUTION: Granville and Preston are 550 miles apart. A car leaves Preston bound for Granville; at the same time, another car leaves Granville bound for Preston, traveling 10 mph faster than

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Question 269593: Granville and Preston are 550 miles apart. A car leaves Preston bound for Granville; at the same time, another car leaves Granville bound for Preston, traveling 10 mph faster than the other car. If they meet after 5 hours, find the speed of each car.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write equations for each:
d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
given:
t%5B1%5D+=+5 hrs
t%5B2%5D+=+5 hrs
r%5B2%5D+=+r%5B1%5D+%2B+10 mi/hr
d%5B1%5D+%2B+d%5B2%5D+=+550 mi
-----------------------
(1) d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
(1) d%5B1%5D+=+r%5B1%5D%2A5
(1) 5r%5B1%5D+-+d%5B1%5D+=+0
-----------------------
(2) d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
(2) 550+-+d%5B1%5D+=+%28r%5B1%5D+%2B+10%29%2A5
(2) 550+-+d%5B1%5D+=+5r%5B1%5D+%2B+50
(2) 5r%5B1%5D+%2B+d%5B1%5D+=+500
------------------------
Add (1) and (2)
(1) 5r%5B1%5D+-+d%5B1%5D+=+0
(2) 5r%5B1%5D+%2B+d%5B1%5D+=+500
10r%5B1%5D+=+500
r%5B1%5D+=+50 mi/hr
And, since
r%5B2%5D+=+r%5B1%5D+%2B+10
r%5B2%5D+=+50+%2B+10
r%5B2%5D+=+60 mi/hr
The 1st car goes 50 mi/hr, the 2nd car goes 60 mi/hr
check:
(2) 550+-+d%5B1%5D+=+%28r%5B1%5D+%2B+10%29%2A5
(2) 550+-+d%5B1%5D+=+%2850+%2B+10%29%2A5
(2) 550+-+d%5B1%5D+=+300
(2) d%5B1%5D+=+250 mi
and
(2) d%5B2%5D+=+r%5B2%5D%2A5
(2) d%5B2%5D+=+60%2A5
(2) d%5B2%5D+=+300
and
d%5B1%5D+%2B+d%5B2%5D+=+550
OK