SOLUTION: A bus trip of 90 miles would have taken an hour less if the average speed had been increased by 3 miles per hour. Find the usual average speed of the bus.

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Question 1010050: A bus trip of 90 miles would have taken an hour less if the average speed had been increased by 3 miles per hour. Find the usual average speed of the bus.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the average speed of the bus
(1) +90+=+s%2At+
(2) +90+=+%28+s+%2B+3+%29%2A%28+t+-+1+%29+
-------------------------
(2) +90+=+t%2A%28+s+%2B+3+%29+-+s+-+3+
and
(1) +t+=+90%2Fs+
Substitute (1) into (2)
(2) +90+=+%28+90%2Fs+%29%2A%28+s+%2B+3+%29+-+s+-+3+
(2) +93+=+%28+90%2Fs+%29%2A%28+s+%2B+3+%29+-+s+
(2) +93+=+90+%2B+270%2Fs+-+s+
(2) +3+=+270%2Fs+-+s%0D%0AMultiply+both+sides+by+%7B%7B%7B+s+
(2) +3s+=+270+-+s%5E2+
(2) +s%5E2+%2B+3s+-+270+=+0+
Use quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+3+
+c+=+-270+
+s+=+%28-3+%2B-+sqrt%28+3%5E2+-+4%2A1%2A%28-270%29+%29%29+%2F+%282%2A1%29+
+s+=+%28-3+%2B-+sqrt%28+9+%2B+1080+%29%29+%2F2+
+s+=+%28-3+%2B+33+%29+%2F2+
+s+=+30%2F2+
+s+=+15+
The usual speed is 15 mi/hr
------------------------
check:
(1) +t+=+90%2Fs+
(1) +t+=+90%2F15+
(1) +t+=+6+ hrs
and
(2) +90+=+%28+s+%2B+3+%29%2A%28+t+-+1+%29+
(2) +90+=+%28+15+%2B+3+%29%2A%28+t+-+1+%29+
(2) +90+=+18t+-+18+
(2) +18t+=+108+
(2) +t+=+6+
OK