A plane left 30 minutes late than it's scheduled time and in order to reach the destination 1500kms away in time,it had to increase it's speed by 100km/hr from the usual speed.find it's usual speed.
Answers
Answer:
- Usual speed of train is 500 km/h.
Explanation:
Let, usual speed of Plane be x km/h
given that, it has to cover a distance of 1500 km
then, using formula; time = distance / speed
time taken by plane to reach the destination will be,
- 1500 / x km/h
Now,
when plane left 30 min means 1/2 hrs late from the scheduled time, then it has to increase its speed by 100 km/h to reach the destination on time.
hence, new speed of plane = x + 100 km/h
and new time taken by plane to reach the destination on time will be
- 1500 / ( x + 100 ) km/h
so,
→ 1500/x - 1500/(x+100) = 1/2
taking LCM in LHS
→ (1500 ( x + 100 ) - 1500 x)/(x² + 100 x) = 1/2
→ (1500 x + 150000 - 1500 x)/(x² + 100 x) = 1/2
→ 150000/(x² + 100 x) = 1/2
cross multiplying
→ 300000 = x² + 100 x
→ x² + 100 x - 300000 = 0
→ x² + 600 x - 500 x - 300000 = 0
→ x ( x + 600 ) - 500 ( x + 600 ) = 0
→ ( x - 500 ) ( x + 600 ) = 0
→ x = 500 or x = -600
since, speed cannot be negative,
therefore,
- Usual speed of plane will be 500 km/h .