Question

10. A takes 3 h more than B in walking 30 km. If A doubles his speed, he will take 2 h less than B.
Assuming the speed of A to be x km/h, obtain an equation. Also, find the speeds of A and B.​

Answer 1

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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———–(i)

When A doubles his speed, then the time taken by A = 30/2x

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

30/y – 30/2x = 3/2

30/y – 15/x = 3/2————–(ii)

Let us assume that 1/x = p & 1/y = q

So equation (i) and equation (ii) becomes

30p – 30q = 3——–(iii)

30q – 15p = 3/2——–(iv)

On adding equation (ii) and (iv) we get,

30p – 30q = 3

+ (-15p) + 30q = 3/2

_________________

15p = 9/2

p = 9/(2×15)

p = 3/10

Substituting the value of p = 3/10 in equation(iii) we get

30p – 30q = 3

30(3/10) – 30q = 3

9 – 30q = 3

-30q = -6

q = 1/5

Now we know that , 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