in a flight of 6000 km ,an aircraft was slowed down due to bad weather .its average speed for the trip was reduced by 400km/hr and time increased by 30mins .find theoriginal duration of the flight
 

Asked by ndsharma24 | 10th Dec, 2015, 08:24: PM

Expert Answer:

T o t a l space d i s tan c e space g i v e n equals 6000 space k m L e t space apostrophe t apostrophe space b e space t h e space o r i g i n a l space d u r a t i o n space o f space t h e space f l i g h t. T h u s comma space o r i g i n a l space s p e e d space o f space t h e space f l i g h t equals 6000 over t T h e space s p e e d space f o r space t h e space t r i p space w a s space r e d u c e d space b y space 400 space k m divided by h r space a n d space t i m e space i n c r e a s e d space b y space 30 space m i n s. T h u s comma space n e w space s p e e d equals fraction numerator 6000 over denominator t plus begin display style 1 half end style end fraction D i f f e r e n c e space i n space s p e e d equals 400 space k m divided by h r rightwards double arrow 6000 over t minus fraction numerator 6000 over denominator t plus begin display style 1 half end style end fraction equals 400 rightwards double arrow fraction numerator 6000 open parentheses t plus 1 half close parentheses minus 6000 t over denominator t open parentheses t plus 1 half close parentheses end fraction equals 400 rightwards double arrow fraction numerator 6000 cross times 1 half over denominator t open parentheses t plus 1 half close parentheses end fraction equals 400 rightwards double arrow 3000 equals 400 t open parentheses t plus 1 half close parentheses rightwards double arrow 3000 equals 400 t squared plus 200 t rightwards double arrow 400 t squared plus 200 t minus 3000 equals 0 rightwards double arrow 2 t squared plus t minus 15 equals 0 rightwards double arrow 2 t squared plus 6 t minus 5 t minus 15 equals 0 rightwards double arrow 2 t open parentheses t plus 3 close parentheses minus 5 open parentheses t plus 3 close parentheses equals 0 rightwards double arrow open parentheses 2 t minus 5 close parentheses open parentheses t plus 3 close parentheses equals 0 rightwards double arrow open parentheses 2 t minus 5 close parentheses equals 0 space o r space open parentheses t plus 3 close parentheses equals 0 rightwards double arrow t equals 5 over 2 space o r space t equals negative 3 T i m e space c a n n o t space b e space n e g a t i v e. T h u s comma t equals 5 over 2 space h o u r equals 5 over 2 cross times 60 equals 150 space m i n u t e s

Answered by Vimala Ramamurthy | 11th Dec, 2015, 10:33: AM

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