SOLUTION: Two towns have a distance of 224 km. How long to reach the town if by travelling 6 kph faster, the trip is reduced by 1 hr.

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Question 662490: Two towns have a distance of 224 km. How long to reach the town if by travelling 6 kph faster, the trip is reduced by 1 hr.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the normal speed in km/hr
Let +t+ = time to reach town at normal speed in hrs
given:
+s+%2B+6+ = faster speed
+t+-+1+ = time to reach town at faster speed
-----------
Equation for normal speed:
(1) +224+=+s%2At+
Equation for faster speed:
(2) +224+=+%28+s+%2B+6+%29%2A%28+t+-+1+%29+
---------------------------
(1) +s+=+224%2Ft+
Substitute (1) into (2)
(2) +224+=+%28+224%2Ft+%2B+6+%29%2A%28+t+-+1+%29+
(2) +224+=+224+%2B+6t+-+224%2Ft+-+6+%7D%7D%0D%0A%282%29+%7B%7B%7B+0+=+6t+-+224%2Ft+-+6+
(2) +224%2Ft+=+6t+-+6+
Multiply both sides by +t+
(2) +224+=+6t%5E2+-+6t+
(2) +3t%5E2+-+3t+-+112+=+0+
Use quadratic formula to solve
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+-3+
+c+=+-112+
+t+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2+-+4%2A3%2A%28-112%29+%29%29+%2F+%282%2A3%29+
+t+=+%28+3+%2B-+sqrt%28+9+%2B+1344+%29%29+%2F+6+
+t+=+%28+3+%2B-+sqrt%28+1353+%29%29+%2F+6+
+t+=+%28+3+%2B+36.783+%29+%2F+6+
+t+=+6.631+
It normally takes 6.631 hrs to reach town
or 6 hrs 38 min
check:
(1) +224+=+s%2At+
(1) +224+=+s%2A6.631+
(1) +s+=+33.78+
and
(2) +224+=+%28+s+%2B+6+%29%2A%28+6.631+-+1+%29+
(2) +224+=+%28+s+%2B+6+%29%2A5.631+
(2) +s+%2B+6+=+39.78+
(2) +s+=+33.78+
OK