Question

Sanjay and Sonia start from a given point and travel by car on a straight road at an average speed of 30 km and 50 km per hour respectively. Sanjay starts at 10 am and Sonia starts 3 hours later. Find the time when Sonia meets Sanjay.

Answer 1

Hint:
Here we will first assume the time taken by Sanjay to cover a distance. Then we will equate the distance travelled by Sanjay to the distance travelled by Sonia to get the value of assumed time. Then we will add this time to the starting time of Sanjay to get the time when Sonia meets Sanjay.

Complete step by step solution:
It is given that the average speeds of 30 km and 50 km per hour of Sanjay and Sonia respectively.
Let the time taken for which Sanjay to cover a distance be \[t\] hours.
It is given that Sonia starts 3 hours later than Sanjay. Then according to the given condition, time taken for Sonia to drive a car to cover a distance will be \[t - 3\] hours.
Now, it is given that the two cars start from the same point and they will meet again when they have covered equal distances.
Therefore, on equating the distance travelled by Sanjay and Sonia, we get
\[ \Rightarrow 30 \times t = 50 \times \left( {t - 3} \right)\]
Now by solving this we will get the value of the time taken \[t\], we get
\[ \Rightarrow 30t = 50t - 150\]
\[ \Rightarrow 50t - 30t = 150\]
Subtracting the like terms, we get
\[ \Rightarrow 20t = 150\]
Dividing 150 by 20, we get
\[ \Rightarrow t = \dfrac{{150}}{{20}} = 7.5{\rm{hours}}\]
So, the time taken by Sanjay to cover the distance is 7 hours and 30 minutes
Hence, the time when Sonia meets Sanjay is equals to \[ = 10:00{\rm{hours}} + 7:30{\rm{hours}} = 17:30{\rm{hours}}\]
We know that \[17:30{\rm{hours}}\] is equal to \[5:30PM\].

Hence, Sonia meets Sanjay at \[5:30PM\].

Note:
We know that the distance is equal to the product of the speed and time. Speed is the distance which is traveled in some particular amount of time. We should not get confused speed with velocity. Speed is a scalar quantity, whereas velocity is a vector quantity as velocity is the ratio of the displacement to the time taken to travel that distance of displacement.
The formula of speed is given by \[{\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}}\].
The formula of velocity is given by \[{\rm{velocity}} = \dfrac{{{\rm{displacement}}}}{{{\rm{time}}}}\].