Question 58

The distance covered by a train in $$(x + 1)$$ hours is $$( x^3 + 1)$$ km. What is the speed of the train?

Solution

Given,

Distance covered by the train = $$( x^3 + 1)$$ km

Time taken by the train = $$(x+1)$$ hours

Speed of the train = $$\frac{\text{Distance covered}}{\text{Time taken}}$$

$$=\frac{\left(x^3+1\right)}{\left(x+1\right)}$$

$$=\frac{\left(x+1\right)\left(x^2-x+1\right)}{\left(x+1\right)}$$

$$=\left(x^2-x+1\right) km/h$$

Hence, the correct answer is Option C

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