Question

WPR:- A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

Standard:- 10

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Answer 1

HELLO !!!...

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●let the original rate of walking be x km/hr and the distance covered be y km.

●therefore time taken to cover y km = distance/speed = y / x hr

therefore,

==>if he walks 1/2 km/hr faster , he takes 1 hour less, therefore eq is:

$\frac{y}{x + \frac{1}{2} } = \frac{y}{x} - 1 \\ \\ \frac{2y}{2x + 1} = \frac{y}{x} - 1 \\ \\ \frac{2y}{2x + 1} = \frac{y - x}{x} \\ \\ 2xy = 2xy + y - 2 {x}^{2} - x \\ \\ y = 2 {x}^{2} + x \: \: \: \: \: \: - - - - - - - - (1)$



==> if he walks 1 km / hr slower, he takes 3 more hours:

$\frac{y}{x - 1} = \frac{y}{x} + 3 \\ \\ \frac{y}{x - 1} = \frac{y + 3x}{x} \\ \\ xy = (x - 1)(y + 3x) \\ \\ xy = xy - y + 3 {x}^{2} - 3x \\ \\ y = 3 {x}^{2} - 3x \: \: \: \: \: \: - - - - - - - - (2)$


●from eq(1) and eq(2):-

$2 {x}^{2} + x = 3 {x}^{2} - 3x \\ \\ {x}^{2} - 4x = 0 \\ \\ x(x - 4) = 0 \\ \\ x = 0 \: \: \: or \: \: \: \: x = 4$


since x is the speed , it can not be zero, therefore rate of walking = 4 km/hr

and,
$y = 3 \times {4}^{2} - 3 \times 4 = 3 \times 16 - 12$


y = 48-12 = 36 km

thus the distance covered is 36 km.


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hope this helps you.

Good night ☺☺

Sweet dreams ➖➖

# Nikky