Question

50 points

A takes 3 hrs more than B to walk a distance of 30 km. but if A doubles his speed he is ahead of B by 1.5 hrs . Find the speed of A and B​​

Answer 1

SOLUTION ☺️

=) Speed of A= x

=) Speed of B= y

Distance= 30km

1st case

$= > \frac{30}{x} = \frac{30}{y} + 3 \\ = > \frac{30}{x} - 3 = \frac{30}{y} ............(1)$

2nd Case

$= > \frac{30}{x} = \frac{30}{y } - \frac{3}{2} \\ = > \frac{30}{x} + \frac{3}{2} = \frac{30}{y} ..........(2) \\ = > from \: (1) \: and \: (2) \\ = > \frac{30}{x} - 3 = \frac{30}{x} + \frac{3}{2} \: \: \: (axiom \: 1) \\ = > \frac{30}{x} - \frac{30}{2x} = \frac{3}{2} + 3 \\ = > \frac{60x - 30x}{2 {x}^{2} } = \frac{3 + 6}{2} \\ = > \frac{30x}{ {x}^{2} } = 9 \\ = > 30x = 9 {x}^{2} \\ = > 9x = 30 \\ = > x = \frac{30}{9} = \frac{10}{3} km \: per \: hour$

Speed of A= 10/3 km/hrs

Substitute in Equation (1)

$= > \frac{ \frac{30}{10} }{3} - 3 = \frac{30}{y} \\ = > 9 - 3 = \frac{30}{y} \\ = > 6 = \frac{30}{y} \\ = > 6y = 30 \\ = > y = \frac{30}{6} \\ = > y = 5 \: km \: per \: hours$

Speed of B= 5 km/hrs

HOPE it helps ✔️☺️

Answer 2

Answer:

Let speed of A = x km/h

Speed of B = y km/h

Distance = 30 km

Time taken by A to walk 30 km =

distance /speed = 30/x hr

Time taken by B to walk 30 km = 30/yhr

According to the given condition,

30/x + 30/y = 3

Dividing both side by 3 we get,

10/x + 10/y = 1 ----------(1)

If A double his speed he is ahead of B by 1.5 hr means 3/2 hr.

When A double his speed = 2x km/hr

Time taken by A to walk 30 km = 30/2x hr

According to the given condition,

30/y = 30/2x + 3/2

Dividing both side by 3/2 we get,

20/y = 10/x + 1 ----------(2)

Put 1/x = a & 1/y = b

From eqn.(1) 10a = 10b +1

10a - 10b = 1 ------------(3)

From eqn. (2) 20b= 10a + 1

10a - 20b = -1 ------------(4)

Subtracting eqn. (4) from eqn. (3) we get,

10a - 10b -(10a - 20b) = 1-(-1)

10a - 10b - 10a + 20b = 2

10b = 2

b = 2/10

b = 1/5

1/y = 1/5

y = 5

Put the value of b in eqn. (3) we get,

10a -10 ×1/5 = 1

10a -2 = 1

10a = 1 + 2

10a = 3

a = 3/10

1/x = 3/10

x = 10/3

Speed of A = 10/3 km/hr

Speed of B = 5 km/hr

Hope it helps! ! !