Question

Two cars start together in the same direction from the same place. The first goes with a uniform speed of 10 km/h. The second goes at a speed of 8km/h in the first hour and increase the speed by 1/2 km each succeeding hour. After how many hours will the second car overtake the first, if both go non stop.?
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Please try solved explanation. ​

Answer 1

Let the second car meets the first car after n hours.

Second car starts with 8km/h, After succeeding hours his speed increases by 0.5 km.

So, Distance travelled by second car = 8 + 8.5 + 9

..... 8+(n-1) 0.5.....(1)

eqn. (1) sum of n terms Of A.P with first term 8

and common difference 0.5.

Sum of all the terms in equation 1 is also equals to the distance travelled by the first car for n hours, i.e. 10n km .

Now, we have (n/2) {16+(n-1) 0.5} = 10n........(2)

From equation (2) we get, n= 9

Hence, Both the cars will meet after 9 hours.

Hope it helps!