This question is similar to Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Cross Multiplication Method

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https://www.teachoo.com/11663/502/Ex-3.5--4-iv/category/Ex-3.5/

 

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Question 32 (B) Places A and B are 180 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at different speeds, they meet in 9 hours. If they travel towards each other with the same speeds as before, they meet in an 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 180 km 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 = 180 km Distance travelled by 1st car – Distance travelled by 2nd car = 180 km Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒 Distance = Speed × Time (Speed of first car × 9 hours) – (Speed of 2nd car × 9 hours) = 180 km 9x – 9y = 180 9(x – y) = 180 (x – y) = 180/9 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 = 180 km Distance travelled by 1st car + Distance travelled by 2nd car = 180 km Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒 Distance = Speed × Time (Speed of first car × 1 hours) + (Speed of 2nd car × 1 hours) = 100 km x + y = 180 So, our two equations are x – y = 20 …(1) x + y = 180 …(2) From (1) x – y = 20 x = y + 20 Putting value of x in (2) x + y = 180 (y + 20) + y = 180 2y + 20 = 180 2y = 180 – 20 2y = 160 y = 160/2 y = 80 Putting y = 80 in equation (1) x – y = 20 x – 80 = 20 x = 80 + 20 x = 100 Therefore x = 100, y = 80 is the solution Thus, Speed of first car = x km/hr = 100 km/hr Speed of second car = y km/hr = 80 km/hr

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.