Question

A man travels to his office by a car at a speed of 40 Km/hr. and reaches 9 min late. If he drives a car at a speed of 50 Km/hr. he reached 6 min early. What is the distance between his office and his home?

Answer 1

Hint: In this particular type of question use the concept that speed is the ratio of distance to time so assume any variable be the actual distance between his office and his home and another variable be the actual time taken then construct the linear equation according to given condition so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Let the distance between his office and his home be x meters.
Now let the actual time by the man to cover x meters be t mins.
Now it is given that a man travels to his office by a car at a speed of 40 Km/hr. and reaches 9 min late.
So the time taken by the man = (t + 9) min.
And the speed (v) = 40 Km/hr.
As we know that, 1 Km = 1000m and 1hr = 60min.
So 40 Km/hr = 40 (1000/60) m/min = (2000/3) m/min.
Now as we know that speed is the ratio of distance to time so we have,
$ \Rightarrow \dfrac{{2000}}{3} = \dfrac{x}{{t + 9}}$.................. (1)
Now it is also given that if he drives a car at a speed of 50 Km/hr. he reached 6 min early.
So this time speed = 50 Km/hr = 50 (1000/60) = (2500/3) m/min.
And the time taken by the man = (t – 6) min.
Therefore,
$ \Rightarrow \dfrac{{2500}}{3} = \dfrac{x}{{t - 6}}$............... (2)
Now from equation (1) calculate the value of t in terms of x we have, $ \Rightarrow \left( {t + 9} \right) = \dfrac{{3x}}{{2000}}$
$ \Rightarrow t = \dfrac{{3x}}{{2000}} - 9$
Now substitute this value in equation (2) we have,
$ \Rightarrow \dfrac{{2500}}{3} = \dfrac{x}{{\dfrac{{3x}}{{2000}} - 9 - 6}}$
Now simplify it we have,
$ \Rightarrow \dfrac{{2500}}{3} = \dfrac{x}{{\dfrac{{3x}}{{2000}} - 15}}$
$ \Rightarrow \dfrac{{2500}}{3}\left( {\dfrac{{3x}}{{2000}} - 15} \right) = x$
$ \Rightarrow \dfrac{{25}}{{20}}x - 2500\left( 5 \right) = x$
$ \Rightarrow \dfrac{5}{4}x - 12500 = x$
$ \Rightarrow \dfrac{5}{4}x - x = 12500$
$ \Rightarrow \dfrac{{\left( {5 - 4} \right)}}{4}x = 12500$
$ \Rightarrow x = 12500\left( 4 \right) = 50000$m.
So x = 50 Km.
So the distance between his office and his home is 50 Km.
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is that first construct the linear equation according to first given condition as above then construct another linear equation according to second given condition as above then simplify it using substitution method as above we will get the required distance between his office and his home.