SOLUTION: Two cars leave from a city at the same time and travel in the same direction. One car travels two and two-thirds times as fast as the other. After 1 hour, they are 50 miles apart.

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Question 888635: Two cars leave from a city at the same time and travel in the same direction. One car travels two and two-thirds times as fast as the other. After 1 hour, they are 50 miles apart. What are the speeds of the cars? Write and solve a system of equations.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the slower car
+%28+8%2F3+%29%2As+ = the speed of the faster car
Let +d+ = the distance the faster car travels in +1+ hr
+50+-+d+ = the distance the slower car travels in +1+ hr
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Equation for slower car:
(1) +50+-+d+=+s%2A1+
Equation for faster car:
(2) +d+=+%28+8%2F3+%29%2As%2A1+
----------------------
Substitute (2) into (1)
(1) +50+-+%28+8%2F3+%29%2As+=+s+
(1) +150+-+8s+=+3s+
(1) +11s+=+150+
(1) +s+=+13+636+ mi/hr
+%28+8%2F3%29%2As+=+%28+8%2F3+%29%2A%28+150%2F11+%29+
+%28+8%2F3+%29%2As+=+36.364+ mi/hr
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The faster car's speed is 36.364 mi/hr
The slower car's speed is 13.636 mi/hr
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check:
(1) +50+-+d+=+s%2A1+
(1) +50+-+d+=+150%2F11+
(1) +d+=+550%2F11+-+150%2F11+
(1) +d+=+400%2F11+
and
(2) +d+=+%28+8%2F3+%29%2As%2A1+
(2) +d+=+%28+8%2F3+%29%2A%28+150%2F11+%29+
(2) +d+=+400%2F11+
OK