a group of students and their sports teacher for going from Delhi to Mumbai for an inter school competition by plane due to some Technology problem the plane left 50 minutes later than its scheduled time and in order to reach the nation thousand 1250 km away in time the pilot lead to increase its speed by 250 km per hour from its usual speed find its usual speed
Answers
Given, aeroplane left 50 minutes later than its schedule time,
and in order to reach the destination, 1250 km away, in time,
it had to increase its speed to 250 km / hr. from its usual speed.
Let the usual speed be ‘a’.
Increased speed = a + 25
As speed increases time decreases
So according to question,
⇒ 6 × 1250 × (a + 250 –a) = 5(a2 + 250a)
⇒ a2 + 250a – 375000 = 0
⇒ a2 + 750a – 500a – 375000 = 0
⇒ a(a + 750) – 500(a + 750) = 0
⇒ (a + 750) (a – 500) = 0
⇒ a = 500 km/hr
Hence the usual speed is 500 km/hr.
The normal speed of plane is 500 kmph
1) Let the original speed of airplane be X kmph.
2) Distance covered by plane = 1250km.
3) Time taken in normal case would be = 1250/x hrs.
4) Increased speed = x+250 kmph
5) Time taken in this case = 1250/(x+250) hrs.
6) The delay caused = 50 min = 5/6 hrs.
7) 1250/x -(1250/(x+250)) = 5/6
8) solving for X:
1250(1/x - 1/(x+250)) = 5/6
1250(250/(x*(x+250))) = 5/6
9) Hence, x= 500 kmph.