SOLUTION: The time for the bus trip between two towns is 45 minutes shorter than the time for the train trip between the same two towns. if the towns are 360 km apart and the train speed is

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Question 908581: The time for the bus trip between two towns is 45 minutes shorter than the time for the train trip between the same two towns. if the towns are 360 km apart and the train speed is 15km/h slower than that of bus, find the speed of the bus in km/h.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for the train to
travel between the towns
+t+-+3%2F4+ = time in hrs for the bus
to travel between the towns
Let +s+ = the speed of the bus in km/hr
+s+-+15+ = the speed of the train in km/hr
--------------------------------------
Equation for bus:
(1) +360+=+s%2A%28+t+-+3%2F4+%29+
Equation for train:
(2) +360+=+%28+s+-+15+%29%2At+
------------------------
(1) +360+=+s%2At+-+%283%2F4%29%2As+
(1) +1440+=+4%2As%2At+-+3s+
and
(2) +t+=+360%2F%28+s+-+15+%29+
-------------------------
Substitute (2) into (1)
(1) +1440+=+4%2As%2A%28+360+%2F+%28+s+-+15+%29+%29+-+3s+
(1) +1440%2A%28+s+-+15+%29+=+1440s+-+3s%2A%28+s+-+15+%29+
(1) +1440s+-+21600+=+1440s+-+3s%5E2+%2B+45s+
(1) +3s%5E2+-+45s+-+21600+=+0+
(1) +s%5E2+-+15s+-+7200+=+0+
use quadratic equation:
+s+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-15+
+c+=+-7200+
+s+=+%28+-%28-15%29+%2B-+sqrt%28+%28-15%29%5E2+-+4%2A1%2A%28-7200%29+%29%29+%2F+%282%2A1%29+
+s+=+%28+15+%2B-+sqrt%28+225+%2B+28800+%29%29+%2F+2+
+s+=+%28+15+%2B-+sqrt%28+29025+%29%29+%2F+2+
+s+=+%28+15+%2B+170.367+%29+%2F+2+
+s+=+185.367+%2F+2+
+s+=+92.684+
the speed of the bus was 92.68 km/hr
check:
(2) +360+=+%28+s+-+15+%29%2At+
(2) +360+=+%28+92.68+-+15+%29%2At+
(2) +360+=+77.68t+
(2) +t+=+4.63+ hrs
and
(2) +360+=+%28+s+-+15+%29%2At+
(2) +360+=+%28+92.68+-+15+%29%2A4.63+
(2) +360+=+77.68%2A4.63+
(2) +360+=+359.66+
Looks close enough- error due
to rounding off