Question

While covering distance of 30 km. Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit. Find their speeds of walking.

Answer 1

The Speed of Ajeet is 5  km/h

The Speed of Amit is 7.5  km/h

Step-by-step explanation:

Given as :

Total distance to be cover by Ajeet  and Amit = D = 30 km

Let The speed of Ajeet = x km/h

Let The Speed of Amit = y km/h

Time taken by Amit = t hours

Time taken by Ajeet = (t + 2) hours

According to question

∵ Time = $\dfrac{Distance}{Speed}$

For Amit

  t = $\dfrac{30}{y}$             ......1

For Ajeet

  t + 2 = $\dfrac{30}{x}$        .....2

From eq 1 and eq 2

$\dfrac{30}{y}$ + 2 = $\dfrac{30}{x}$

Or, $\dfrac{30}{x}$ - $\dfrac{30}{y}$  = 2

i.e  $\dfrac{1}{x}$  - $\dfrac{1}{y}$  = $\dfrac{2}{30}$

∴  $\dfrac{1}{x}$  - $\dfrac{1}{y}$  = $\dfrac{1}{15}$                     ........3

Again

Ajeet doubles his speed, he would take 1 hour less than Amit.

So, Speed of Ajeet = 2 x km/h

      Time taken by Amit = t  h

∴     Time aken by Ajeet = ( t - 1 ) h

Now,

For Amit

  t = $\dfrac{30}{y}$             ......4

For Ajeet

  t - 1 = $\dfrac{30}{2x}$        .....5

From eq 4 and 5

$\dfrac{30}{y}$ - 1 =  $\dfrac{30}{2x}$

Or,  $\dfrac{30}{y}$  - $\dfrac{30}{2x}$  =  1

∴  $\dfrac{1}{y}$  - $\dfrac{1}{2x}$  = $\dfrac{1}{30}$           .............6

Again

solving eq 3 and 6

$\dfrac{1}{x}$  - $\dfrac{1}{y}$  = $\dfrac{1}{15}$  

$\dfrac{1}{y}$  - $\dfrac{1}{2x}$  = $\dfrac{1}{30}$      

Or, ( $\dfrac{1}{y}$  - $\dfrac{1}{2x}$  ) + ( $\dfrac{1}{x}$  - $\dfrac{1}{y}$ ) = $\dfrac{1}{30}$  +  $\dfrac{1}{15}$

Or,  ( $\dfrac{1}{y}$ - $\dfrac{1}{y}$ )  + ( $\dfrac{1}{x}$ - $\dfrac{1}{2x}$ ) = $\dfrac{1+2}{30}$

Or,  0 + ( $\dfrac{2 -1}{2x}$ )  = $\dfrac{3}{30}$

Or,    $\dfrac{1}{2x}$   = $\dfrac{1}{10}$

by cross multiplication

2 x = 10

∴ x = $\dfrac{10}{2}$

i.e x = 5 km/h

So, The Speed of Ajeet = x = 5  km/h

Put the value of x in eq 3

$\dfrac{1}{5}$  - $\dfrac{1}{y}$  = $\dfrac{1}{15}$  

Or, $\dfrac{1}{y}$ = $\dfrac{1}{5}$ - $\dfrac{1}{15}$

Or, $\dfrac{1}{y}$  = $\dfrac{3-1}{15}$

Or, $\dfrac{1}{y}$  =  $\dfrac{2}{15}$

i.e  y = $\dfrac{15}{2}$  = 7.5 km/h

So, The Speed of Amit = y = 7.5  km/h

Hence, The Speed of Ajeet is 5  km/h

And  The Speed of Amit is 7.5  km/h   Answer