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CBSE Class 10 Answered

Two cars start together in the same direction from the same place. The first goes with uniform speed of 10km/hr. The second goes at a speed of 8km/hr in the first hour and increases its speed by 1/2 km/hr each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?
Asked by rushabh123 | 17 Feb, 2019, 20:20: PM
answered-by-expert Expert Answer
Let the second car meets the first car after n hours.
 
second car starts with 8km/hr. After succeeding hours its speed increases by 0.5 km
 
Then distance travelled by second car = 8 + 8.5 + 9.0 +................8+(n-1)0.5 ................................(1)
 
eqn.(1) sum of n terms of Arithmetic progression with first term 8 and common difference 0.5
 
sum of all the terms in eqn.(1) is also equals to the distance travelled by first car for n hours, i.e., 10n km
 
hence we have, (n/2) [ 16 + (n-1)0.5 ] = 10 n  .................(2)
 
from eqn.(2), we get n = 9.
 
Hence both the car will meet after 9 hours.
Answered by Thiyagarajan K | 17 Feb, 2019, 20:33: PM

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