SOLUTION: dave travels a distance 216 km by train and returns by a car which travels at an average speed of 9kph faster then the train. if the total journey takes 14 hours, find the average

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Question 953717: dave travels a distance 216 km by train and returns by a car which travels at an average speed of 9kph faster then the train. if the total journey takes 14 hours, find the average speed of the train and the car, respectively/
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Dave's speed in km/hr in train
+s+%2B+9+ = Dave's speed in km/hr in car
Let +t+ = Dave's time in hrs in train
+14+-+t+ = Dave's time in hrs in car
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Equation for train:
(1) +216+=+s%2At+
Equation for car:
(2) +216+=+%28+s+%2B+9+%29%2A%28+14+-+t+%29+
-----------------------------
(2) +216+=+14s+%2B+126+-+s%2At+-+9t+
(2) +90+=+s%2A%28+14+-+t+%29+-+9t+
and
(1) +s+=+216%2Ft+
Substitute (1) into (2)
(2) +90+=+%28+216%2Ft+%29%2A%28+14+-+t+%29++-+9t+
(2) +90+=+3024%2Ft+-+216+-+9t+
(2) +9t+%2B+306+-+3024%2Ft+=+0+
Multiply both sides by +t+
(2) +9t%5E2+%2B+306t+-+3024+=+0+
(2) +t%5E2+%2B+34t+-+336+=+0+
Use the quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+34+
+c+=+-336+
+t+=+%28+-34+%2B-+sqrt%28+34%5E2+-+4%2A1%2A%28-336%29+%29%29+%2F+%282%2A1%29+
+t+=+%28+-34+%2B-+sqrt%28+1156+%2B+1344+%29%29+%2F+2+
+t+=+%28+-34+%2B-+sqrt%28+2500+%29%29+%2F+2+
+t+=+%28+-34+%2B+50%29+%2F+2+
+t+=+16%2F2+
+t+=+8+
--------------
(1) +s+=+216%2Ft+
(1) +s+=+216%2F8+
(1) +s+=+27+
and
+s+%2B+9+=+36+
+27+%2B+9+=+36+
---------------------
The speed of the train is 27 km/hr
The speed of the car is 36 km/hr
---------------------
check:
(2) +216+=+%28+27+%2B+9+%29%2A%28+14+-+8+%29+
(2) +216+=+36%2A6+
(2) +216+=+216+
OK