Question

a plane left 30 minutes late than its scheduled time in order to reach the destination 2,500 km away in time it had to increase its speed by 100 km per hour from the used speed . find its usual speed

Answer 1

Answer:

658.87 km/Hr

Step-by-step explanation:

Let say usual speed =  x km/hr

Distance = 2500 km

Time taken with usual speed = 2500/x  hr

Increased speed = x+100 km

Time taken with increased speed = 2500/(x+100) hr

2500/x   -  2500/(x+100)  = 1/2

2500(x+100) - 2500x = x(x+100)/2

5000 * 100 = x^2 +  100x

x^2 + 100x  = 500000

x^2 + 100x + 2500 = 500000 +2500

(x + 50)^2 = 5025000

x + 50 = 708.87

x = 708.87 - 50

x = 658.87

usual speed = 658.87 km/Hr

Answer 2

Let usual speed=xkmph
Also time taken =d/s
2500/x
Now in IInd case speed increased=100kmph
So time taken=2500/x+100
Acc. To question,
2500/x-2500/x+100=1/2
2500x+250000-2500x/x2+100x=1/2
500000=x2+100x
X2+100x-500000=0
Root d =b2-4ac
100×100+4×500000
2010000=1417. 7
X=-b+-root d/2a
X=1317.7/2=658.85kmph