Two cyclists start together in the same direction from the same place. The first goes with uniform speed of 10km per hour. The second goes at a speed of 8 km per hour in the first hour and increases the speed ½ km each succeeding hour. After how many hours the second cyclist overtake the first if both go non-stop?
Answers
Answered by
86
Speed of first cyclist = 10 km/h
Speed of second cyclist:
In the first hour = 8km/h
In second hour = (8+1/2) = 17/2 km/h
In third hour = (17/2 + 1/2) = 9 km/h
The numbers 8,17/2,9....are in AP
In which a = 8, d = 1/2 and n = x
Let the second cyclist overtake first cyclist in x hours.
∴ Distance covered by the first cyclist in x hours.
= distance covered by the second cyclist in x hours.
= 10x = sum of x numbers in above AP = Sₓ
∴ 10x = x/2[2a+(x-1)d]
∴ 10x = x/2[2*8+(x+1)1/2]
∴ 10x*2/x = 16 + x/2 -1/2
∴ 2*20 = 32+x-1
∴ 40 - 31 = x
x = 9
∴ The second cyclist overtake the first cyclist in 9 hours.
Speed of second cyclist:
In the first hour = 8km/h
In second hour = (8+1/2) = 17/2 km/h
In third hour = (17/2 + 1/2) = 9 km/h
The numbers 8,17/2,9....are in AP
In which a = 8, d = 1/2 and n = x
Let the second cyclist overtake first cyclist in x hours.
∴ Distance covered by the first cyclist in x hours.
= distance covered by the second cyclist in x hours.
= 10x = sum of x numbers in above AP = Sₓ
∴ 10x = x/2[2a+(x-1)d]
∴ 10x = x/2[2*8+(x+1)1/2]
∴ 10x*2/x = 16 + x/2 -1/2
∴ 2*20 = 32+x-1
∴ 40 - 31 = x
x = 9
∴ The second cyclist overtake the first cyclist in 9 hours.
duragpalsingh:
click on thanks link above
what is AP
(x-1)1/2 change + into -
can u explain equation clearly
Answered by
4
Answer:
9 hours
Step-by-step explanation:
9 hours
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