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

Answer:

Speed Of A is 10/3 km/hr. Speed of B is 5 km/hr.

Step-by-step explanation:

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= r  and 1/y = s

so eqs 1 & 2 become ,then On adding eq 3 & 4

30r -  30s = 3……….(3)

-15r +  30s = 3/2………(4)

---------------------------

15 r = 3 + 3/2

15 r =( 6 + 3)/2 = 9/2

15r = 9/2

r = 9 /(2×15) = 3/10

r = 3/10

On Putting the value of r = 3/10 in eq 3

30r -  30s = 3

30 (3/10) - 30s = 3

9 - 30s = 3

9 - 3 = 30s

6 = 30s

s = 6/30= 1/5

1/y = s             [ Let 1/y = s]

1/y = ⅕

y = 5 km/h.

1/x = r           [Let 1/x= r]

1/x = 3/10

x = 10/3 km/h.

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