Question

Speed of first car is 10 km/hr and the speed
of IInd car is 8 km/hr. The 2nd car increases
its speed 1/2 km/hr after each hour. After
how much distance the second overtake the
first?
(A) 90 km (B) 100 km
(C) 180 km (D)NOT

Answer 1

Answer:

90 km

Step-by-step explanation:

Consider the second car overtake the first car after t hours.

∴ Distance covered by first car = distance covered by second car.

10t = 8 + ( 8 + 1/2 ) + ( 8 + 2/2) + ( 8 + 3/ 2) + --------------------+ ( 8 + (t - 1) / 2)

10t = 8t + (1/2) [ 1 + 2 + 3 + ................+ ( t - 1)]

2t = (1/2)[ t (t -1) / 2]

8t = [ t2 - t ]

t2 = 9t

∴ t = 9 as t ≠ 0

∴ the second car overtake the first car by 9 hours.

Distance = speed of first car x time taken to overtake

Distance = 10 X 9 =90 KM