4. A passenger train takes 2 hours more than an express train to travel a distance of 240 km from Wardha to Akola. The speed of the passenger train is less than the express train by 20 km/hr. Find the average speed of both the trains.
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Step-by-step explanation:
Velocity of passenger train=V
p
Velocity of express train=V
e
Time taken by passenger train =t
p
Time taken by express train =t
e
Distance traveled, s=V
p
t
p
=V
e
t
e
=240km
240=V
p
t
p
=(V
p
+20)(t
p
−2)
240=V
p
t
p
=V
p
t
p
−2V
p
+20t
p
−40
240=−2V
p
+20(
V
p
240
)−40
240V
p
=−2V
p
2
+4800−40V
p
−2V
p
2
−280V
p
+4800=0
2V
p
2
+280V
p
−4800=0
V
p
2
+140V
p
−2400=0
V
p
=
2
−140±
140
2
+4×2400
V
p
=15.44km/h (speed cannot be negative)
V
e
=V
p
+20=35.44km/h
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