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.
Answers
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
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
According to statement,
After 3 hours they are 500 km apart.
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.