Question

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?

Answer 1

Step-by-step explanation:

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Speed of first cyclist  = 10 km/hSpeed of second cyclist:In the first hour = 8km/hIn second hour = (8+1/2) = 17/2 km/hIn third hour = (17/2 + 1/2) = 9 km/hThe numbers 8,17/2,9....are in APIn which a = 8, d = 1/2 and n = xLet 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]

8+(x+1)1/2]∴ 10x×2/x = 16 + x/2 -1/2

2/x = 16 + x/2 -1/2∴ 2×20 = 32+x-1

20 = 32+x-1∴ 40 - 31 = x

20 = 32+x-1∴ 40 - 31 = xx = 9

Answer 2

Given :-

• Two cyclists start together in the same direction from the same place.
• Speed of First cyclist = 10km/h.
• Speed of Second cyclist = 8km/h. in the first hour and increases the speed ½ km each succeeding hour....

To Find :-

• After how many hours the second cyclist overtake the first if both go non-stop ?

Solution :-

Lets First Understand The Question :-

The Cyclist whose speed is slow, will Travel 8km in first hour, 8.5 km in second hour, 9 km in Third hour _______________ Upto He overtake The First cyclist. (AP series).

Now, Let us Assume That, after t hours Second Cyclist overtake The first cyclist.

So, we can say That, Distance Travel by Them in t hours will be same before overtake.. ( As they Travel from Same Point).

So,

→ Distance Travel by Slower = Distance Travel by Faster.

→ Sum of t terms of AP = 10 * t

→ (t/2)[2a + (t - 1)d ] = 10t

→ (t/2)[2*8 + (t - 1)0.5 ] = 10t

→ [ 16 + 0.5t - 0.5 ] = 20

→ 15.5 + 0.5t = 20

→ 0.5t = 20 - 15.5

→ 0.5t = 4.5

→ t = (4.5/0.5)

→ t = 9 Hours.

Hence, The second cyclist overtake the first after 9 hours.