SOLUTION: scooter travels 12 miles in the same time that a bicycle covers 5 miles. if the rate of the scooter is 2 mph more than twice the rate of the bicycle find both rates

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Question 1029768: scooter travels 12 miles in the same time that a bicycle covers 5 miles. if the rate of the scooter is 2 mph more than twice the rate of the bicycle find both rates
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hrs for
both scooter and bicycle
Let +r+ = the rate of the bicycle in mi/hr
+2r+%2B+2+ = the rate of the scooter in mi/hr
-------------------------------------
Equation for the bicycle:
(1) +5+=+r%2At+
Equation for the scooter:
(2) +12+=+%28+2r+%2B+2+%29%2At+
---------------------
(1) +t+=+5%2Fr+
Substitute this result into (2)
(2) +12+=+%28+2r+%2B+2+%29%2A%28+5%2Fr+%29+
Multiply both sides by +r+
(2) +12r+=+10r+%2B+10+
(2) +2r+=+10+
(2) +r+=+5+
and
+2r+%2B+2+=+2%2A5+%2B+2+
+2r+%2B+2+=+12+
--------------------
The rate of the bicycle is 5 mi/hr
The rate of the scooter is 12 mi/hr
-----------------------------
check:
(1) +5+=+r%2At+
(1) +5+=+5%2At+
(1) +t+=+1+ hr
and
(2) +12+=+%28+2r+%2B+2+%29%2At+
(2) +12+=+%28+2%2A5+%2B+2+%29%2At+
(2) +12+=+12t+
(2) +t+=+1+ hr
OK