Check sibling questions

A train covered a certain distance at uniform speed. If train 10 km

Ex 3.7, 3 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Ex 3.7, 3 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3 Ex 3.7, 3 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4 Ex 3.7, 3 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 5 Ex 3.7, 3 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 6

This video is only available for Teachoo black users

Maths Crash Course - Live lectures + all videos + Real time Doubt solving!


Transcript

Ex 3.7, 3 A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train. Let Speed of train = x km/h & Time taken = y hours. We know that, Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒 Distance = Speed × Time Distance = xy If the train would have been 10 km/h faster I.e. Speed = x + 10 It would have taken 2 hours less i.e. Time = y − 2 Now, Distance = Speed × time Distance = (x + 10) (y − 2) Putting Distance = xy from Equation (1) xy = (x + 10) (y − 2) xy = x (y − 2) + 10 (y − 2) xy = xy − 2x + 10y − 20 2x − 10y + 20 = xy − xy 2x − 10y + 20 = 0 Also, If the train were slower by 10 km/h Speed = x − 10, it would have taken 3 hours more Time = y + 3. Now Distance = Speed × time Distance = (x − 10) (y + 3) Putting Distance = xy from equation (1) xy = (x − 10) (y + 3) xy = x (y + 3) − 10y − 30 xy = xy + 3x − 10y − 30 xy − xy = 3x − 10y − 30 3x − 10y − 30 = 0 Hence, the equations are 2x − 10y + 20 = 0 …(2) 3x − 10y − 30 = 0 …(3) From equation (2) 2x − 10y + 20 = 0 2 (x − 5y + 10) = 0 x − 5y + 10 = 0 x = 5y − 10 Putting (4) in equation (3) 3x − 10y − 30 = 0 3 (5y − 10) − 10y − 30 = 0 15y − 30 − 10y − 30 = 0 5y − 60 = 0 5y = 60 y = 60/5 y = 12 Putting y = 12 in equation (4) x = 5y − 10 x = (5 × 12) − 10 x = 60 − 10 x = 50 Thus, Speed of train = x = 50 km/ h & Time taken by the train = y = 12 hours Now, Distance = Speed × time Distance = 50 × 12 Distance = 600 km

Ask a doubt (live)
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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.