Question

In covering a distance of 30 km , Hari takes 2 hrs more than Ram . If Hari doubles his speed , he would take 1 hr less than Ram. what is the speed of Hari?​

Answer 1

Speed

To calculate the speed, we need to know the Distance and time. That is, Distance in metres (m) and Time in seconds (s), so the units will be in metres per second (m/s).

${\boxed{\bullet\:{Speed\:=\:{\dfrac{Distance}{Time}}}}}$

As we went through the concept about Speed, Now, Let's move on finding the solution for our question.

We have given that, In covering a total distance of 30 km, Hari takes 2 hrs more than Ram . If Hari doubles his speed , he would take 1 hr less than Ram. And we have been asked to find the speed of Hari.

Let,

• Speed of Hari be 'a'
• Speed of Ram be 'b'

We know that,

• Total Distance = 30 km

According to the condition,

Condition 1 : Hari takes 2 hrs more than Ram,

$\sf\implies{{\dfrac{30}{a}}\:=\:2\:+\:{\dfrac{30}{b}}}\:---(1)$

Condition 2 : If Hari doubles his speed, he would take 1 hr less than Ram,

$\sf\implies{{\dfrac{30}{2(a)}}\:=\:{\dfrac{30}{b}}\:-\:1}\:---(2)$

Subtracting (1) & (2), we get,

$\sf\implies[{{\dfrac{30}{a}}\:=\:2\:+\:{\dfrac{30}{b}}}]\:-\:[{\dfrac{30}{2(a)}}\:=\:{\dfrac{30}{b}}\:-\:1]$

$\sf\implies[{{\dfrac{30}{a}}\:=\:2\:+\:{\cancel{{\dfrac{30}{b}}}}}]\:-\:[{\dfrac{30}{2(a)}}\:=\:{\cancel{{\dfrac{30}{b}}}}\:-\:1]$

$\sf\implies{{\dfrac{30}{2(a)}}\:=\:2\:+\:1}$

$\sf\implies{{\dfrac{30}{2(a)}}\:=\:3}$

$\sf\implies{30\:=\:3\:\times\:2a}$

$\sf\implies{30\:=\:6a}$

$\sf\implies{a\:=\:{\dfrac{30}{6}}}$

$\sf\implies{a\:=\:{\cancel{{\dfrac{30}{6}}}}}$

$\sf\implies{a\:=\:5}$

Hence, the speed of Hari = 5 km/hr.