SOLUTION: A car travels for 100 miles at a uniform speed. If the speed is increased by 5 miles per hour, the trip would take one hour less time. what is the car's original speed?

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Question 880137: A car travels for 100 miles at a uniform speed. If the speed is increased by 5 miles per hour, the trip would take one hour less time. what is the car's original speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +100+=+r%2At+
(2) +100+=+%28+r%2B5+%29%2A%28+t-1+%29+
--------------------------
(1) +t+=+100%2Fr+
By substitution:
(2) +100+=+%28+r+%2B+5+%29%2A%28+100%2Fr+-+1+%29+
(2) +100+=+100+%2B+500%2Fr+-+r+-+5+
(2) +r+%2B+5+=+500%2Fr+
(2) +r%5E2+%2B+5r+=+500+
(2) +r%5E2+%2B+5r+%2B+%28+5%2F2%29%5E2+=+500+%2B+%285%2F2%29%5E2+
(2) +r%5E2+%2B+5r+%2B+25%2F4+=+2000%2F4+%2B+25%2F4+
(2) +r%5E2+%2B+5r+%2B+25%2F4+=+2025%2F4+
(2) +%28+r+%2B+5%2F2+%29%5E2+=+%28+45%2F2+%29%5E2+
(2) +r+%2B+5%2F2+=+45%2F2+
(2) +r+=+40%2F2+
(2) +r+=+20+
The car's original speed was 20 mi/hr
check:
(1) +100+=+r%2At+
(1) +100+=+20t+
(1) +t+=+5+
and
(2) +100+=+%28+r%2B5+%29%2A%28+t-1+%29+
(2) +100+=+%28+20%2B5+%29%2A%28+t-1+%29+
(2) +100+=+25t+-+25+
(2) +25t+=+125+
(2) +t+=+5+
OK