A plane left 30 minutes late than its scheduled
time and in order to reach the destination 1500
km away in time, it had to increase speed by
100 km/h from the usual speed. Find its usual speed.
Answers
Answer:
Let the usual speed be x km/hr.
Then, the speed taken =(x+100) km/hr
Distance =1500 km
Usual time =
usual speed
distance
=
x
1500
hrs
Time taken =
x+100
1500
hrs
It is given that Time taken=Usual time−0.5 hrs
⇒
x
1500
−
x+100
1500
=
2
1
⇒
x(x+100)
1500(x+100)−1500x
=
2
1
⇒x
2
+100x=1500×100×2
⇒x
2
+100x−300000=0
⇒x=
2
−100±
100
2
+4×300000
=
2
−100±1100
=500 or−600
Since speed cannot be negative, x=500 km/hr
∴ The usual speed of the plane is 500 km/hr.
Answer:
Let the usual speed be x km/hr.
Then, the speed taken =(x+100) km/hr
Distance =1500 km
Usual time =
usual speed
distance
=
x
1500
hrs
Time taken =
x+100
1500
hrs
It is given that Time taken=Usual time−0.5 hrs
⇒
x
1500
−
x+100
1500
=
2
1
⇒
x(x+100)
1500(x+100)−1500x
=
2
1
⇒x
2
+100x=1500×100×2
⇒x
2
+100x−300000=0
⇒x=
2
−100±
100
2
+4×300000
=
2
−100±1100
=500 or−600