A plane left 30 minutes late than the schedule time and in order to reach its destination 1500 km away in time,it has to increase its speed by 100 km/h from its usual speed.find its usual speed.
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Secondary SchoolMath 10+5 pts
A plane left 30 minutes late than the schedule time and in order to reach its destination 1500 km away in time,it has to increase its speed by 100 km/h from its usual speed.find its usual speed.
Report by Potty2potty 27.03.2018
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abhi178
Abhi178 The Sage
Let sedule time is T.
Then speed of aeroplane = distance covered/time taken = 1500km/T hour ---(1)
A/C to question,
Time taken by Aeroplane in 2nd case = sedule time - 30 minutes
= (T - 1/2) hour
Now, speed of aeroplane = distance covered/time taken = 1500/(T - 1/2) ----(2)
Now, 1500/(T - 1/2) - 1500/T = 100 [according to question]
1500[ (T - T + 1/2)/(T² - T/2)] = 100
15×1/2 = T² - T/2
15 = 2T² - T
2T² - T - 15 = 0
2T² - 6T + 5T - 15 = 0
T = 3 and -5/2 , T ≠ -5/2 so, T = 3
Hence, usual speed of aeroplane = 1500/T = 1500/3 = 500 I'm/h
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