Question 15

Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars.       1. Class 10
2. Solutions of Sample Papers for Class 10 Boards
3. CBSE Class 10 Sample Paper for 2019 Boards

Transcript

Question 15 Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars. Let the speed of first car be x km/hr and speed of second car be y km/hr If travelling in same direction Time = 8 hours Distance travelled by 1st car = AC Distance travelled by 2nd car = BC Difference of distance travelled = AC – BC = (AB + BC) – BC = AB = 80 km Therefore, Distance travelled by 1st car – Distance travelled by 2nd car = 80 km Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒 Distance = Speed × Time 8x – 8y = 80 8 (x – y) = 80 x – y = 80/8 x – y = 10 …(1) 1 mark If travelling in opposite direction Time = 1 hours 20 minutes = 1 + 20/60 hours = 1 + 1/3 = 4/3 hours Distance travelled by 1st car = AC Distance travelled by 2nd car = BC Now, Total distance travelled = AC + BC = AB = 80 km Therefore, Distance travelled by 1st car + Distance travelled by 2nd car = 80 km Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒 Distance = Speed × Time 4/3x + 4/3y = 80 4/3 (x + y) = 80 x + y = 80 × 3/4 x + y = 60 …(2) 1 mark Thus, our equations are x – y = 10 …(1) x + y = 60 …(2) Adding (1) & (2) (x – y) + (x + y) = 10 + 60 2x = 70 x = 70/2 x = 35 Putting value of x in (2) x + y = 60 35 + y = 60 y = 60 – 35 y = 25 So, Speed of first car = x = 35 km/hr Speed of second car = 25 km/hr 1 mark

CBSE Class 10 Sample Paper for 2019 Boards

Class 10
Solutions of Sample Papers for Class 10 Boards 