Question

A train travels a distance of 480 km at a uniform speed. If the speed had been
8 km/h less, then it would have taken 3 hours more to cover the same distance. We
need to find the speed of the train.express in quardatic equation​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Let the speed of the train be x km/hr. Then

Time taken to travel a distance of 480km= 480/x hr.

Time taken by the train to travel a distance of 480km with the speed (x−8)km/hr= 480/x−8

hr.

It is given that if the speed had been 8km/hr less, then the train would have taken 3 hours more to cover the same distance

∴

$\frac{480}{x - 8} = \frac{480}{x} + 3 \\ \frac{480}{x - 8} - \frac{480}{x} = 3 \\ \frac{480 \times 8}{x(x - 8)} = 3 \\ \frac{480 \times 8}{x(x - 8)} = 3 \\ 3x(x - 8) = 480 \times 8 \\ x(x - 8) = 160 \times 8 \\ {x}^{2} - 8x - 120 = 8$

This is the required quadratic equation.