SOLUTION: Two trains each make a journey of 330km. One of the trains travels 5km/h faster than the other and takes 30 minutes less time. Find the speeds of the trains. Solve by forming an

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Question 581690: Two trains each make a journey of 330km. One of the trains travels 5km/h faster than the other and takes 30 minutes less time. Find the speeds of the trains.
Solve by forming and solving a suitable quadratic equation.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ =the speed of the slower train
Let +t+ = the time for the slower train
-------------
Slower train:
(1) +330+=+s%2At+
faster train:
(2) +330+=++%28+s+%2B+5+%29%2A%28+t+-+.5+%29+
--------------------------
(2) +330+=+s%2At+%2B+5t+-+.5s+-+2.5+
(1) +t+=+330%2Fs+
Substitute this into (2)
(2) +330+=+s%2A%28330%2Fs%29+%2B+5%2A%28330%2Fs%29+-+.5s+-+2.5+
Multiply both sides by s
(2) +330s+=+330s+%2B+1650+-+.5s%5E2+-+2.5s+
(2) +.5s%5E2+%2B+2.5s+-+1650+=+0+
(2) +5s%5E2+%2B+25s+-+16500+=+0+
(2) +s%5E2+%2B+5s+-+3300+=+0+
Use the quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+5+
+c+=+-3300+
+s+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A1%2A%28-3300%29+%29%29+%2F+%282%2A1%29+
+s+=+%28-5+%2B-+sqrt%28+25+%2B+13200+%29%29+%2F+2+
+s+=+%28-5+%2B-+sqrt%28+13225+%29%29+%2F+2+
+s+=+%28+-5+%2B-+115+%29+%2F+2+ ( ignore the negative root )
+s+=+%28+-5+%2B+115+%29+%2F+2+
+s+=+110%2F2+
+s+=+55+
+s+%2B+5+=+60+
55 km/hr is the speed of the slower train
60 km/hr is the speed of the faster train
check:
(1) +330+=+s%2At+
(1) +330+=+55%2At+
(1) +t+=+6+ hrs
(2) +330+=++%28+55+%2B+5+%29%2A%28+t+-+.5+%29+
(2) +330+=++60%2A%28+t+-+.5+%29+
(2) +330+=+60t+-+30+
(2) +60t+=+360+
(2) +t+=+6+ hrs
OK