a train covers a distance of 450 km in 6 hour and 15 minute a if it cover two third of the distance at a speed for 80 km per hour at what speed will be to cover the rest of the distance
Answers
Answer:
Let original speed =xkm/hr
⇒ Time taken to travel =
x
90
hr
⇒ New speed =(x+15)km/hr
⇒ Time taken to travel =
x+15
90
hr
∴
x
90
=
x+15
90
+
2
1
⇒
x
90
−
x+15
90
=
2
1
⇒ 90(
x
1
−
x+15
1
)=
2
1
⇒
x(x+15)
x+15−x
=
180
1
⇒ 15×180=x(x+15)
⇒ 2700=x
2
+15x
⇒ x
2
+15x−2700=0
⇒ x
2
+60x−45x−2700=0
⇒ x(x+60)−45(x+60)=0
⇒ (x+60)(x−45)=0
Speed can not be negative.
∴ The original speed of the train is 45km/hr
Answer:
The train will cover rest of the distance with speed 60 km/h.
Step-by-step explanation:
Given: Total distance that the train covers = 450 km
Total time taken = 6 hour 15 minutes = 6 + 15/60 = 6 + 0.25 = 6.25 hours
Also, the train covers 2/3 of the total distance at a speed of 80 km/h.
⇒ 2/3 of total distance = 450 × 2/3 = 300 km
w.k.t., Speed = (Distance travelled) / (Time taken)
⇒ Time taken to complete 2/3 of the total distance = Distance / Speed
⇒ t = 300 / 80
⇒ t = 3.75 hours
So, remaining distance to be travelled = 450 - 300 = 150 km
Also, time in which this much distance should be covered = 6.25 - 3.75 = 2.50 hours
⇒ Speed with which remaining distance is to be covered = 150 / 2.5 = 60 km/h