A train travels at a certain average speed for a distance of 120 km and then travels a distance of 130 km at an average speed of 5 km/hr more than its original speed. If it takes 4 hours to complete the total journey, then average speed of train during 130km journey and if original speed is decreased by 10 km/hr and is constant in whole journey, then the. time taken. by the train to complete the journey is?
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1
Answer:
42 km/h
Step-by-step explanation:
Let, the original average speed be x km/hr.
Time taken at a speed of x km/hr (t
1
)=
x
63
hrs
Time taken at a speed of x+6 km/hr (t
2
)=
x+6
72
hrs
t
1
+t
2
=3
x
63
+
x+6
72
=3
⟹
x(x+6)
63((x+6)+72x
=3
⟹63x+378+72x=3x(x+6)
⟹378+135x=3x
2
+18x
⟹3x
2
+18x−135x−378=0
⟹3x
2
−117x−378=0
⟹3(x
2
−39x−126)=0
⟹x
2
−39x−126=0
⟹x
2
−42x+3x−126=0
⟹x(x−42)+3(x−42)=0
⟹(x−42)(x+3)=0
Either x=42 or x=−3
∵ speed cannot be negative. x=42 is considered.
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