Question

A takes 3 hours more than B to walk a distance of 30 km. But, if A doubles his pace (speed) he is ahead of B by 1 1/2 hours. Find the speeds of A and B.

Answer 1

The speed of A is  $\dfrac{10}{3}$km/h

The speed of B is 5 km/h  

Step-by-step explanation:

Given as :

The distance to be travel by A and B = D = 30 km

Let The speed of A = x km/h

Let The speed of B = y km/h

∵ Distance = Speed × Time

Time = $\dfrac{distance}{speed}$

3 = $\dfrac{30}{x}$ -  $\dfrac{30}{y}$               ........1

Again

The speed of A = 2 x  km/h  , A is ahead of B by  1.5 hours

Time = $\dfrac{distance}{speed}$

∴  1.5  = $\dfrac{30}{y}$  -  $\dfrac{30}{2x}$             ......2

Let $\dfrac{1}{x}$ = m

And  $\dfrac{1}{y}$  = n

Substituting the value in eq 1 and eq 2

30 m - 30 n = 3                 ......3

30 n - 15 m = 1.5                 .......4

Solving eq 3 and eq 4

( 30 m - 30 n ) + 2 × ( 30 n - 15 m ) = 3 + 2 × 1.5

Or, ( 30 m - 30 m) + ( 60 n - 30 n ) = 3 + 3

Or,  0 + 30 n = 6

∴    n = $\dfrac{6}{30}$

i.e  n = $\dfrac{1}{5}$

∵  $\dfrac{1}{y}$  = n

i.e   $\dfrac{1}{y}$   = $\dfrac{1}{5}$

Or,  y = 5

So, The speed of B = y = 5 km/h

Put the value of n in eq 3

∵ 30 m - 30 ×$\dfrac{1}{5}$  = 3

Or, 30 m - 6 = 3

Or, 30 m = 9

or, 10 m = 3

∴     m = $\dfrac{3}{10}$

∵  $\dfrac{1}{x}$  = m

i.e   $\dfrac{1}{x}$   = $\dfrac{3}{10}$

Or,  x = $\dfrac{10}{3}$

So, The speed of A = x =  $\dfrac{10}{3}$km/h

Hence,  The speed of A is  $\dfrac{10}{3}$km/h

And  The speed of B is 5 km/h        Answer

Answer 2

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Step-by-step explanation: