SOLUTION: A tractor has a rear wheel with a circumference of x m. The circumference of the front wheel is 6m less. If the front wheel makes 10 more revolutions than the rear wheel every 360m

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Question 1150456: A tractor has a rear wheel with a circumference of x m. The circumference of the front wheel is 6m less. If the front wheel makes 10 more revolutions than the rear wheel every 360m, what is the circumference, in m, of the front wheel?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x+ = circumference of rear wheel in meters
+x+-+6+ = circumference of front wheel in meters
Let +360%2Fr+ = meters traced on ground for
each revolution of the rear wheel
+360%2F%28+r+%2B+10+%29+ = meters traced on ground for
each revolution of the front wheel
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+360%2Fr+=+x+
(1) +r+=+360%2Fx+
and
+360%2F%28+r+%2B+10+%29+=+x+-+6+
(2) +r+%2B+10+=+360%2F%28+x+-+6+%29+
Plug (1) into (2)
(2) +360%2Fx+%2B+10+=+360%2F%28+x+-+6+%29+
Multiply both sides by +x%2A%28+x+-+6+%29+
(2) +360%2A%28+x+-+6+%29+%2B+10x%2A%28+x+-+6+%29+=+360x+
(2) +360x+-+2160+%2B+10x%5E2+-+60x+=+360x+
(2) +10x%5E2+-+60x+-+2160+=+0+
(2) +x%5E2+-+6x+-+216+=+0+
(2) +%28+x+-+18+%29%2A%28+x+%2B+12+%29+=+0+
The circumference of the rear wheel is 18 m
+x+-+6+=+18+-+6+
+x+-+6+=+12+
The circumference of the front wheel is 12 m
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check answer:
(1) +r+=+360%2Fx+
(1) +r+=+360%2F18+
(1) +r+=+20+
and
(2) +r+%2B+10+=+360%2F%28+x+-+6+%29+
(2) +r+%2B+10+=+360%2F+12+
(2) +r+%2B+10+=+30+
(2) +r+=+20+
OK