Sum

Two cars start together in the same direction from the same place. The first cargoes 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?

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#### Solution

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= `10xxn km` Distance travelled by the 2^nd car in n hours=`n/2[2xx8+(n-1)xx0.5]km`

`⇒ 10xxn=n/2[2xx8+(n-1)xx0.5]`

`⇒20=16+0.5n-0.5`

`⇒0.5n=4.5`

`⇒n=9`

Thus , the two cars will meet after 9 hours.d08

Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms.

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