Problem 9.1. Vanya runs from home to school at a constant speed. If he had initially increased his speed by 2 m/s, he would have arrived at school 2.5 times faster. How many times faster would he have arrived at school if he had initially increased his speed by 4 m/s?

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# Answer: 4.

Solution. Let Vasya's initial speed be $v$ m/s. If he ran at a speed of $(v+2)$ m/s, he would cover the same distance to school 2.5 times faster. This means that $\frac{v+2}{v}=2.5$, from which we find $v=\frac{4}{3}$. If he had initially run at a speed of $(v+4)$ m/s, he would have arrived at school $\frac{v+4}{v}$ times faster. Substituting $v=\frac{4}{3}$ into this expression, we get the answer 4.