Two cars start together in same direction from the same place the first goes with uniform speed of 10km/hr . The second goes at a speed of 8km/hr by 1/2km/h in each succeeding hour . After how many hours will the second car overtake the first. If both cars go non - stop

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Solution

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[28+(x+1)1/2]

∴ 10x2/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.

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