Rajeev started to move from point A towards point B exactly an hour after Rohit started from B in the opposite direction but at a speed twice as much as that of rohit.By the time rohit covers ⅙ of the distance between the point B and A Rajeev also covers the same distance.

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2022-03-04T11:38:16+01:00

Speed is the rate of change of distance over time

It takes Rohit 2 hours to cover the same distance

Represent Rajeev with A, and Rohit with B

Speed is calculated as:

[tex]Speed = \frac{Distance}{Time}[/tex]

Rohit covers 1/6 of the distance between point AB

So, we have:

[tex]S_B = \frac{AB/6}{T_B}[/tex]

Make T the subject

[tex]T_B = \frac{AB/6}{S_B}[/tex]

[tex]T_B = \frac{AB}{6S_B}[/tex]

Rajeev's speed is twice that of Rohit.

So, we have:

[tex]S_A = 2 * S_B[/tex]

[tex]S_A = \frac{AB}{T_A}[/tex]

So, the time taken by Rajiv to cover 1/6 of the distance is:

[tex]T_A = \frac{AB}{12S_B}[/tex]

The difference between the time is given as 1.

So, we have:

[tex]\frac{AB}{6S_B} - \frac{AB}{12S_B} = 1[/tex]

Multiply through by 12SB

[tex]2AB - AB = 12S_B[/tex]

[tex]AB = 12S_B[/tex]

Recall that:

[tex]T_B = \frac{AB}{6S_B}[/tex]

So, we have:

[tex]T_B =\frac{12S_B}{6S_B}[/tex]

[tex]T_B = 2[/tex]

Hence, it takes Rohit 2 hours to cover the same distance