A takes 3 hours more than B to walk 30 km. But if A doubles his pace he is ahead of B by 3/4 hours.Find their speed of walking
Answers
⊕ANSWER⊕
GIVEN :
Distance = 30 km
Let speed of A be = x km/h & speed of B be = 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 hour 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 hours]
30/y = 30/2x + 3/2
30/y - 30/2x = 3/2
30/y - 15/x = 3/2.............(2)
Let 1/x = p & 1/y = q
So eqn (1) becomes
30p - 30q = 3...............(3)
And eqn (2) becomes
30q - 15p = 3/2..............(4)
On adding equation 3 and 4
30p - 30q = 3
+ (-15p) + 30q = 3/2
_________________
15p = 9/2
p = 9/(2×15)
p = 3/10
On putting the value of p = 3/10 in equation 3
30p - 30q = 3
30(3/10) - 30q = 3
9 - 30q = 3
-30q = -6
q = 1/5
Now, 1/y = q
1/y = 1/5
y = 5km/h
&, 1/x = p
1/x = 3/10
x = 10/3 km/h
Hence
A = 10/3 km/h
B = 5 km/h