Check sibling questions

Places A and B are 100 km apart on a highway. One car starts [Video]

Ex 3.5, 4 (iv) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Ex 3.5, 4 (iv) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3 Ex 3.5, 4 (iv) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4 Ex 3.5, 4 (iv) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 5 Ex 3.5, 4 (iv) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 6 Ex 3.5.jpg

Get live Maths 1-on-1 Classs - Class 6 to 12


Transcript

Ex 3.5, 4 Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : (iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? Let Speed of first car be x km/hr & Speed of second car be y km/hr If travelling in same direction Distance travelled by 1st car = AC = AB + BC Distance travelled by 2nd car = BC Difference of distance travelled = (AB + BC) – BC = AB = 100 km Distance travelled by 1st car – Distance travelled by 2nd car = 100 km (Speed of first car × 5 hours) – (Speed of 2nd car × 5 hours) = 100 km 5x – 5y = 100 5(x – y) = 100 (x – y) = 100/5 x – y = 20 If travelling in opposite direction Distance travelled by 1st car = AD Distance travelled by 2nd car = BD Sum of distance travelled = AD + BD = AB = 100 km Distance travelled by 1st car + Distance travelled by 2nd car = 100 km (Speed of first car × 1 hours) + (Speed of 2nd car × 1 hours) = 100 km x + y = 100 So, our two equations are x – y = 20 …(1) x + y = 100 …(2) From (1) x – y = 20 x = y + 20 Putting value of x in (2) x + y = 100 (y + 20) + y = 100 2y + 20 = 100 2y = 100 – 20 2y = 80 y = 80/2 y = 40 Putting y = 40 in equation (1) x – y = 20 x – 40 = 20 x = 40 + 20 x = 60 Therefore x = 60, y = 40 is the solution Thus, Speed of first car = x km/hr = 60 km/hr Speed of second car = y km/hr = 20 km/hr

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.