please solve this ques - A takes 3 hrs more than B to walk a distance of - Maths - Pair of Linear Equations in Two Variables

Question

please solve this ques - A takes 3 hrs more than B to walk a
distance of 30 km but if A doubles his pace he is ahead of B by one
and half hrs find speed of A and B?

Lalit Mehra · Accepted Answer

Dear Student!

Let the speed of A and B be x km/hr and y km/hr respectively.

We know that,

$T i m e = \frac{Distance}{Speed} ∴ Time taken by A to cover 30 km= \frac{30}{x} Time taken by B to cover 30 km= \frac{30}{y}$

Given, time taken by A = time taken by B + 3 hr

∴ Time taken by A – 3 hr = Time taken by B

$∴ \frac{30}{x} - 3 = \frac{30}{y} \Rightarrow 30 y - 3 x y = 30 x \Rightarrow 30 x - 30 y = - 3 x y \Rightarrow 10 x - 10 y = - x y ... (1) W h e n A d o u b l e s h i s s p e e d, t h e n T i m e t a k e n b y A + \frac{3}{2} h r = T i m e t a k e n b y B (G i v e n) ∴ \frac{30}{2 x} + \frac{3}{2} = \frac{30}{y} \Rightarrow 30 y + 3 x y = 60 x \Rightarrow 60 x - 30 y = 3 x y \Rightarrow 20 x - 10 y = x y ... (2)$

Solving (1) and (2), we get

$20 x - 10 y = + x y 10 x - 10 y = - x y \underset{̲}{- + +} 10 x = 2 x y \Rightarrow y = \frac{10 x}{2 x} = 5$

Putting the value of y in equation (1), we get

$10 x - 50 = - 5 x \Rightarrow 15 x = 50 \Rightarrow x = \frac{50}{15} = \frac{10}{3}$

Thus, the speed of A is $\frac{10}{3} km/hr$ and speed of B is 5 km/hr.

Cheers!

please solve this ques...- A takes 3 hrs more than B to walk a distance of 30 km .but if A doubles his pace he is ahead of B by one and half hrs.find speed of A and B?