Question

A takes 3 hrs more than B to walk a distance of 30 KM but A doubles its speed{pace].he is ahead by 1 and ahalf hrs.find the speed of walking?

Answer 1

GIVEN :
Distance = 30 km

Let speed of A be = x km/h &  speed of B = y km/h.

Time taken by A to cover 30  km = 30/x
[ Time = Distance /speed]

Time taken by B to cover 30 km = 30/y
30/x = 30/y + 3
30/x - 30/y = 3…………(1)
[Given : A takes 3 hours more than B to walk ]

When A doubles his speed then, time taken by A = 30/2x
[Given: time taken by B =  Time taken by A + 3/2 h]
30/y = 30/2x + 3/2
30/y - 30/2x  = 3/2
30/y - 15/x  = 3/2 ……..(2)

Let  1/x= p  and 1/y = q

so eqs 1 & 2 become ,then On adding eq 3 & 4
30p -  30q = 3……….(3)
-15p +  30q = 3/2………(4)
---------------------------
15 p = 3 + 3/2

15 p =( 6 + 3)/2 = 9/2
15p = 9/2
p = 9 /(2×15) = 3/10
p = 3/10

On Putting the value of p = 3/10 in eq 3
30p -  30q = 3
30 (3/10) - 30q = 3
9 - 30q = 3
9 - 3 = 30q
6 = 30q

q = 6/30= 1/5
1/y = q               [ Let 1/y = q]
1/y = ⅕
y = 5 km/h

1/x = p             [Let 1/x= p ]
1/x = 3/10
x = 10/3 km/h

so x = 10/3 km/h. &  y = 5 km/h

Hence, the speed of A is 10/3 km/h & B is 5 km/h.

HOPE THIS WILL HELP YOU….

Answer 2

Speed Is inversely related to time : More time less speed ,Less speed more time"

D= 30 km : X = let x b time taken by B

Speed of B = 30 /x ; speed of A : 30/[x+3]  { A take 3 hours More}

A:B = x/{x+3}  ----------- Eq 1

Also A doubled its  Then  Speed A = 30/x-1.5  , B is same

2A:B = x/[x-1.5] -- eq 2

Solving For x  Eq1 & 2  We get x=6 --->> B = 5kmph , A=10/3

Ratio of A:b = 2:3

Hens Proved Not Me