A passenger train takes 2 hours less for a journey if its speed is increased by 5km/h from its usual speed. It takes 30 minutes more if its speed is decreased by 1km/h. find the speed of the train and the distance covered.
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Answer:
Let the usual speed of the train is x km/h.
D=300 km (Given)
Speed=
Time
Distance
Time=
x
300
After increasing the speed of the train ;
New speed is (x+5) km/h
Time=
x+5
300
Now, difference between the time taken by usual speed and after increasing speed of the train is two hours. Therefore,
x
300
−
x+5
300
=2
⇒300(
x
1
−
x+5
1
)=2
⇒(
x
2
+5x
x+5−x
)=
300
2
⇒
x
2
+5x
5
=
150
1
⇒x
2
+5x−750=0
⇒x
2
+30x−25x−750=0
⇒x(x+30)−25(x+30)=0
⇒(x+30)(x−25)=0
⇒x=25,−30
Ignore the negative value of the speed.
Hence, the usual speed of the train is 25 km/hr.
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