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प्रश्न
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?
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उत्तर
Let the two cars meet after n hours.
That means the two cars travel the same distance in n hours.
Distance travelled by the 1st car in n hours = 10 × n km
Distance travelled by the 2nd 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.
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