SOLUTION: Lara rode her motorcycle 300 miles. If she had averaged 10 mph faster, the trip would have taken 1 hour less time. Find Lara's actual average speed

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Question 888375: Lara rode her motorcycle 300 miles. If she had averaged 10 mph faster, the trip would have taken 1 hour less time. Find Lara's actual average speed
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her actual average speed
Let +t+ = her actual time in hours
------------------------------------
(1) +300+=+s%2At+
(2) +300+=+%28+s+%2B+10+%29%2A%28+t+-+1+%29+
-------------------------------
(2) +300+=+s%2At+%2B+10t+-+s+-+10+
(2) +s%2At+-+s+%2B+10t+=+310+
and
(1) +s+=+300%2Ft+
---------------------
(2) +s%2At+-+s+%2B+10t+=+310+
(2) +%28300%2Ft%29%2At+-+300%2Ft+%2B+10t+=+310+
(2) +10t+-+300%2Ft+%2B+300+=+310+
(2) +10t+-+300%2Ft+=+10+
Multiply both sides by +t+
(2) +10t%5E2+-+300+=+10t+
(2) +10t%5E2+-+10t+=+300+
(2) +t%5E2+-+t+=+30+
(2) +t%5E2+-+t+%2B+%28+1%2F2+%29%5E2+=+30+%2B+%28+1%2F2+%29%5E2+
(2) +t%5E2+-+t+%2B+1%2F4+=+120%2F4+%2B+1%2F4+
(2) +%28+t+-+1%2F2+%29%5E2+=+121%2F4+
take the square root of both sides
(2) +t+-+1%2F2+=+11%2F2+
(2) +t+=+6+
and
(2) +t+-+1%2F2+=+-11%2F2+
(2) +t+=+-5+ ( can't use negative time )
---------------------------------------
(1) +s+=+300%2Ft+
(1) +s+=+300%2F6+
(1) +s+=+50+
Lara's actual average speed was 50 mi/hr
check:
(2) +300+=+%28+s+%2B+10+%29%2A%28+t+-+1+%29+
(2) +300+=+%28+50+%2B+10+%29%2A%28+6+-+1+%29+
(2) +300+=+60%2A5+
(2) +300+=+300+
OK