Question

A metro travels at the speed of 396 km at a uniform speed. If the speed had been 5 km/hr. more, it would have taken 2 hours less for the same journey. What is the speed of the train?

(a) 32 km/hr

(b) 30 km/hr

(c) 20.06 km/hr

(d) 29.06 km/hr

The question was asked in my homework.

This question is from Solution of Quadratic Equation by Squaring Method in chapter Quadratic Equation of Mathematics – Class 10

Answer 1

Right answer is (d) 29.06 km/hr

Best explanation: Let the speed of the metro train be x km/hr

Time taken to cover 396 km at x  km/hr = \(\frac {396}{x}\)  hrs

Time taken to cover 396 km at x+5 km/hr = \(\frac {396}{x+5}\)  hrs

∴ \(\frac {396}{x}-\frac {396}{(x+5)}\)=2

\(\frac {x+5-x}{x(x+5)}=\frac {2}{396}\)

\(\frac {5}{x^2+5x}=\frac {1}{198}\)

990=x^2+5x

x^2+5x=990

Adding \(\frac {b^2}{4}\) on both sides, where b=5

x^2 + 5x + \(\frac {5^2}{4}=\frac {5^2}{4}\) + 990

x^2 + 5x + \(\frac {25}{4}=\frac {25}{4}\) + 990

\((x + \frac {5}{2})\)^2=\((\frac {\sqrt {3985}}{2})\)^2

x + \(\frac {5}{2}\) = ±\(\frac {\sqrt {3985}}{2}\)

x = \(\frac {63.12}{2} -\frac {5}{2}=\frac {58.12}{2}\) = 29.06 and x = \(\frac {-63.12}{2} -\frac {5}{2} = \frac {-68.12}{2}\) = -34.06

Since, speed cannot be negative hence x=29.06 km/hr