passenger train takes 1 hour less when its speed is increased by 15 km per hour. Then its usual speed for a journey of 300 kilometre. Find the usual speed of the train.
Answers
Step-by-step ⇒ Let the usual speed of the train be xkm/hr
⇒ Distance covered in the journey=150km
⇒ Time taken by the train with usual speed =
x
150
hr
⇒ New speed of train =(x+5)km/hr
⇒ Time taken by the train after increasing the speed =
x+5
150
hr
x
150
−
x+1
150
=1
⇒ 150(
x
1
−
x+5
1
)=1
⇒ 150(
x(x+5)
x+5−x
)=1
⇒ 150(5)=x(x+5)
⇒ 750=x
2
+5x
⇒ x
2
+5x−750=0
⇒ x
2
+30x−25x−750=0
⇒ x(x+30)−25(x+30)=0
⇒ (x+30)(x−25)=0
⇒ x+30=0 and x−25=0
⇒ x=−30 and x=25
Speed cannot be negative.
∴ The usual speed of the train is 25km/hr
Answer:
Let the usual speed of the train be xkm/hr
⇒ Distance covered in the journey=150km
⇒ Time taken by the train with usual speed =
x
150
hr
⇒ New speed of train =(x+5)km/hr
⇒ Time taken by the train after increasing the speed =
x+5
150
hr
x
150
−
x+1
150
=1
⇒ 150(
x
1
−
x+5
1
)=1
⇒ 150(
x(x+5)
x+5−x
)=1
⇒ 150(5)=x(x+5)
⇒ 750=x
2
+5x
⇒ x
2
+5x−750=0
⇒ x
2
+30x−25x−750=0
⇒ x(x+30)−25(x+30)=0
⇒ (x+30)(x−25)=0
⇒ x+30=0 and x−25=0
⇒ x=−30 and x=25
Speed cannot be negative.
∴ The usual speed of the train is 25km/hr