SOLUTION: It takes Ricky, traveling at 30 mph, 40 mins longer to go a certain distance than it takes Tyler traveling at 54 mph. Find the distance traveled.

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Question 911407: It takes Ricky, traveling at 30 mph, 40 mins longer to go a certain distance than it takes Tyler traveling at 54 mph. Find the distance traveled.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance in miles traveled
Let +t+ = the time in hours for Tyler to travel +d+ miles
+t+%2B+2%2F3+ = time in hours for Ricky to travel +d+ miles
( Note that +2%2F3+ hrs = +40+ min )
---------------------
Tyler's equation:
+d+=+54t+
Ricky's equation:
+d+=+30%2A%28+t+%2B+2%2F3+%29+
----------------------
By substitution:
+54t+=+30%2A%28+t+%2B+2%2F3+%29+
+54t+=+30t+%2B+20+
+24t+=+20+
+t+=+5%2F6+
---------------
+d+=+54t+
+d+=+54%2A%285%2F6%29+
+d+=+45+
The distance traveled is 45 mi
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check:
+d+=+30%2A%28+t+%2B+2%2F3+%29+
+45+=+30%2A%28+5%2F6%2B+2%2F3+%29+
+45+=+30%2A%28+5%2F6+%2B+4%2F6+%29+
+45+=+30%2A%28+9%2F6+%29+
+45+=+45+
OK