Question

'A' takes 3 hours more than 'B' to walk 30km. But if A doubles his pace, he is ahead of B by 3/2 hours. Find their 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.

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