Question

4. Sanyam travels to his office by a car at a speed of 40 km/hr and reaches
office 9 minutes late. If he drives his car at a speed of 50 km/hr, he reaches
6 minutes early. What is the distance of his office from his home?​

Answer 1

Answer:

Speed = distance / time

Here distance is constant

So, speed is inversely proportional tp time

By using ratio and proportion concept

I have solved the problem.

Answer 2

Given,

The speed of the car in the first case$\[ = 40{\rm{km/hr}}\]$

The speed of the car in the second case$\[ = 50{\rm{km/hr}}\]$

Solution,

Assume that the distance is d and the time is t minutes.

Apply the first condition and calculate the distance.

$\[ \Rightarrow 40 \times \left( {t + 9} \right)\]$

Apply the second condition and calculate the distance.

$\[ \Rightarrow 50 \times \left( {t - 6} \right)\]$

Know that the distance remains the same.

$\[\begin{array}{l} \Rightarrow 40 \times \left( {t + 9} \right) = 50 \times \left( {t - 6} \right)\\ \Rightarrow 40t + 360 = 50t - 300\\ \Rightarrow 50t - 40t = 360 + 300\end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow 10t = 660\\ \Rightarrow t = \frac{{660}}{{10}}\\ \Rightarrow t = 66\end{array}\]$

Therefore, the distance between the office and home is

$\[\begin{array}{l} \Rightarrow 40\left( {9 + 66} \right)\\ \Rightarrow 40 \times 75\\ \Rightarrow 40 \times 1.25\,{\rm{km}}\\ \Rightarrow 50{\rm{km}}\end{array}\]$

Hence, the distance between the office and home is $\[50{\rm{km}}{\rm{.}}\]$