Akhil starts from his gym to his corporate office at certain speed but after 2 hour he resume his journey and become 1 hour 40 min late due to reducing his speed to 3/4 .If Akhil would have met Akhilesh after 70 km then he will be late by 1 hour 15 minutes .Find the actual speed of Akhilesh.
Answers
Answer:
Step-by-step explanation:
Akhil starts from his gym to his corporate office at certain speed but after 2 hour he resume his journey and become 1 hour 40 min late due to reducing his speed to 3/4 .If Akhil would have met Akhilesh after 70 km then he will be late by 1 hour 15 minutes .Find the actual speed of Akhilesh.
Let sat Akhil Speed = x km/Hr
After 2 hrs His speed become 3/4 means 3x/4 km/Hr
Let say he takes time a hr after that then distance covered
Distance = Speed * Time
x * 2 + (3x/4)a
Time taken With Normal Speed = 1 hr 40 min less = (5/3 hrs)
Time taken with normal speed = 2 + a - 5/3 hr
Distance = x * (2 + a - 5/3 )
Equating both distances
x * 2 + (3x/4)a = x * (2 + a - 5/3 )
multiplying with 12
=> 24x + 9ax = 24x + 12ax - 20x
=> 24 + 9a = 24 + 12a - 20
=> 3a = 20
=> a = 20/3
Time taken = with normal speed = 2 + 20/3 - 5/3 = 7 hr
Distance = 2x + (3x/4)(20/3) = 7x
if he would have meet after 70 km then this
then he have lost 1 hr 15 mins only
so he would have saved 25 mins in 70 km
70/(3x/4) - 70/x = 25/60
=> 280/3x - 70/x = 5/12
multiplying by 12x both sides
=> 1120 - 840 = 5x
=> 280 = 5x
=> x = 56
56 km/hr
But if he would have reduced speed after 70 km from start
then time taken is 1 hr 15 min (5/4 hr more than normal)
70/x + (7x-70)/(3x/4) = 7 + 5/4
=> 70/x + 28(x-10)/3x = 7 + 5/4
multiplying by 12x
=> 840 + 112(x-10) = 84x + 15x
=> 840 + 112x - 1120 = 99x
=> 13x = 280
=> x = 280/13 km/hr