Question

Rasheb starts for a wedding venue at 6 pm and drives at a speed of 60 km/hr. Ramesh starts for the same venue at 6.30 pm and drives at a speed of 75 km/hr. When will both reach the venue provided, they reach at the same time?

Answer 1

Hint: We first find the time difference between two people starting their journey. We also assume the time taken by them and use that to find the distance they have covered with their individual speed. That remains constant and gives an equation to solve the problem.

Complete step-by-step answer:
Rasheb starts for a wedding venue at 6 pm and drives at a speed of 60 km/hr. Ramesh starts for the same venue at 6.30 pm and drives at a speed of 75 km/hr.
This means Ramesh started half an hour late which is equal to 30 minutes.
It is given that both of them reach the venue at the same time.
Let us assume that Rasheb reaches the venue in $ t $ hours. This means Ramesh takes $ t-\dfrac{1}{2} $ hours to reach the venue.
The distance they covered is equal for both of them and it is the multiplication of the time with the speed.
Therefore, Rasheb covered $ 60t $ km and Ramesh covered $ 75\left( t-\dfrac{1}{2} \right) $ km.
The equation gives $ 75\left( t-\dfrac{1}{2} \right)=60t $ . Simplifying we get
 $
   75\left( t-\dfrac{1}{2} \right)=60t \\
  \Rightarrow 75t-\dfrac{75}{2}=60t \\
  \Rightarrow 15t=\dfrac{75}{2} \\
  \Rightarrow t=\dfrac{75}{2\times 15}=\dfrac{5}{2} \;
 $
Therefore, $ \dfrac{5}{2} $ hours i.e., 2 hours and 30 minutes from 6 pm will be equal to 8.30 pm. They reach the venue at 8.30 pm.
So, the correct answer is “8.30 pm”.

Note: We also could have used the proportional form to find the extra distance Ramesh has covered if they had used the same amount of time. That gives the extra distance with the extra speed which gives the required time.