Question

Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h^–1. The second car goes at a speed of 8 km h^–1 in the first hour and thereafter increasing the speed by 0.5 km h^–1 each succeeding hour. After how many hours will the two cars meet?

Answer 1

Let the two cars meet after n hours. 

That means the two cars travel the same distance in n hours. 

Distance travelled by the 1^st car in n hours = 10 × n km 

Distance travelled by the 2^nd car in n hours = `n/2[2 xx 8 + (n - 1) xx 0.5]km`       

`\implies 10 xx n = n/2 [2 xx 8 + (n - 1) xx 0.5]`           

`\implies` 20 = 16 + 0.5n – 0.5

`\implies` 0.5n = 4.5

`\implies` n = 9

Thus, the two cars will meet after 9 hours.