Question

Ruma travelled at 7 km/h and missed a train by 7 minutes. However, if she had travelled at 10 km/h, she
would have reached the station 5 minutes before the departure of the train. The distance between her house
and railway station (correct to two decimal places) is:
​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• The distance between house and railway station = x km

We know,

$\rm :\longmapsto\:Time = \dfrac{Distance}{Speed}$

Case :- 1

• Distance travelled = x km

• Speed = 7 km per hour

Time taken to covered 'x' km at the speed of 7 km per hour is

$\rm :\longmapsto\:t_1 = \dfrac{x}{7} \: \: hours$

Case :- 2

• Distance to be covered = x km

• Speed = 10 km per hour

Time taken to cover 'x' km at the speed of 10 km per hour is

$\rm :\longmapsto\:t_2 = \dfrac{x}{10} \: \: hours$

According to statement,

It is observed that time taken to cover 'x' km at the speed of 7 km per hour took 5 + 7 = 12 mins more than that while walking at 10 km per hour.

$\rm :\implies\:t_2 - t_1 = \dfrac{12}{60}$

$\rm :\longmapsto\:\dfrac{x}{7} - \dfrac{x}{10} = \dfrac{12}{60}$

$\rm :\longmapsto\:\dfrac{10x - 7x}{7} = \dfrac{1}{5}$

$\rm :\longmapsto\:\dfrac{3x}{7} = \dfrac{1}{5}$

$\rm :\implies\:x = \dfrac{7}{15} \: km$

$\bf\implies \:x = 0.47 \: km \: (approx)$

Additional Information :-

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.