Question

A girl goes to her friend’s house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, find ‘x’.

Answer 1

We know

${\displaystyle \text{Time}=\frac{\text{Distance}}{\text{Speed}}}$

Given, the girl covers a distance of 6 km at a speed x km/hr.

Time taken to cover first 6 km = ${\displaystyle \frac{6}{x}}$

Also, the girl covers the remaining 6 km distance at a speed (x + 2) km/hr.

Time taken to cover next 6 km = ${\displaystyle \frac{6}{x+2}}$

Total time taken to cover the whole distance = 2 hrs 30 mins

= ${\displaystyle 2\frac{30}{60}}$

= ${\displaystyle 2\frac{1}{2}}$

= ${\displaystyle \frac{5}{2}}$ hrs

${\displaystyle \therefore \frac{6}{x}+\frac{6}{x+2}=\frac{5}{2}}$

${\displaystyle \frac{6x+12+6x}{x(x+2)}=\frac{5}{2}}$

${\displaystyle \frac{12+12x}{x^2+2x}=\frac{5}{2}}$

24 + 24x = 5x² + 10x

5x² – 14x – 24 = 0

5x² – 20x + 6x – 24 = 0

5x(x – 4) + 6(x – 4) = 0

(5x + 6)(x – 4) = 0

${\displaystyle x=\frac{-6}{5},4}$

Since, speed cannot be negative.

Therefore, x = 4.