While covering a 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.

Given:

While covering a distance of 30 km, Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit.
To do:

We have to find the speeds of their walking.

Solution:

Total distance $= 30\ km$

Let the speed of Ajeet be $x\ km/hr$ and the speed of Amit be $y\ km/hr$.

We know that,

$Time=\frac{Distance}{Speed}$

According to the question,

While covering a distance of 30 km, Ajeet takes 2 hours more than Amit.

This implies,

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

$\frac{30}{x}-\frac{30}{y}=2$......(i)

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

This implies,

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

$\frac{15}{x}-\frac{30}{y}=-1$......(ii)

Subtracting equation (ii) from equation (i), we get,

$\frac{30}{x}-\frac{30}{y}-\frac{15}{x}+\frac{30}{y}=2-(-1)$

$\frac{30-15}{x}=2+1$

$\frac{15}{x}=3$

$x=\frac{15}{3}$

$x=5$

Substituting the value of $x=5$ in equation (i), we get,

$\frac{30}{5}-\frac{30}{y}=2$

$6-2=\frac{30}{y}$

$y=\frac{30}{4}$

$y=7.5$

The speed of Ajeet is $5\ km/hr$ and the speed of Amit is $7.5\ km/hr$.

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Updated on: 10-Oct-2022

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