Anjali is practicing cycling for Olympics. She take's certain time to travel a distance of 80km. Had she gone 3km/hr faster. She would have taken 1 hour and 20 minutes less. What time did Anjali take? With working
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let the speed of anjali be x km/hr
so time taken would be 80/x
as time = distance/speed
according to the ques.
80/x - 80/x+3 = 1 integer 20/60
80x+240-80x/x^2+3x = 4/3
720 = 4x^2 + 12x
4(180) = 4(x^2 + 3x)
x^2 + 3x - 180 = 0
by completing the square method
x^2 + 3x + (3/2)^2 - (3/2)^2 - 180 = 0
(x + 3/2)^2 = 9/4 + 180
(x + 3/2)^2 = 9+720/4
(x + 3/2)^2= 729/4
x + 3/2 = √729/4
x + 3/2 = +27/2 , -27/2
taking positive root
x=24/2
x= 12km/hr
since by taking negative root , speed will be coming negative so it will not be considered.
so time taken = 80/12
i.e. 6.66hrs
so time taken would be 80/x
as time = distance/speed
according to the ques.
80/x - 80/x+3 = 1 integer 20/60
80x+240-80x/x^2+3x = 4/3
720 = 4x^2 + 12x
4(180) = 4(x^2 + 3x)
x^2 + 3x - 180 = 0
by completing the square method
x^2 + 3x + (3/2)^2 - (3/2)^2 - 180 = 0
(x + 3/2)^2 = 9/4 + 180
(x + 3/2)^2 = 9+720/4
(x + 3/2)^2= 729/4
x + 3/2 = √729/4
x + 3/2 = +27/2 , -27/2
taking positive root
x=24/2
x= 12km/hr
since by taking negative root , speed will be coming negative so it will not be considered.
so time taken = 80/12
i.e. 6.66hrs
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