Question

There are two cars. the first car is travelling 10 km/hr faster than the second one. they both start at the same spot and at the same time but in opposite direction.in 3 hours they are 500 km apart. solve using system of linear equations.

Answer 1

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

Let assume that both the cars starts from A and after 3 hours, the first car is at B and second car is at C.

It is given that,

Speed of first car is 10 km/hr faster than second car.

So,

Let assume that,

Speed of second car is x km/ hr

and

Speed of first car is x + 10 km/ hr.

Case :- 1 For first car

Speed of car = x + 10 km/ hr

Time to travel = 3 hours

We know, Distance = Speed × Time

So, Distance covered AB in 3 hours at the speed of x + 10 km/hr is

$\boxed{ \sf{ \:AB = 3 \times ( x + 10 ) = 3x + 30 \: km}}$

Case :- 2 For second car

Speed of car = x km/ hr

Time to travel = 3 hours

We know, Distance = Speed × Time

So, Distance covered AC in 3 hours at the speed of x km/hr is

$\boxed{ \sf{ \:AC = 3 \times x = 3x \: km}}$

According to statement,

After 3 hours they are 500 km apart.

$\rm :\longmapsto\:BC = 500 \: km$

$\rm :\longmapsto\:AB \: + \: AC \: = \: 500$

$\rm :\longmapsto\:3x + 30 + 3x = 500$

$\rm :\longmapsto\:6x + 30 = 500$

$\rm :\longmapsto\:6x = 500 - 30$

$\rm :\longmapsto\:6x = 470$

$\rm :\longmapsto\:x = 78.33 \: km \: per \: hour$

So,

Speed of second car = 78. 33 km per hour

and

Speed of first car = 78.33 + 10 = 88. 33 km per hour.

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.