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
Solution:
We will be using the concept of two-variable linear equations to solve the given question.
Let us assume the uniform speed of the train to be x km/h and the time taken to travel the given distance be t hours.
Then distance can be calculated as follows:
Distance = speed × time = xt
Thus, the distance is xt
According to the question,
Condition 1: When the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time.
(x + 10)(t - 2) = xt
xt - 2x + 10t - 20 = xt
- 2x + 10t = 20 ....(1)
Condition 2: When the train would have been slower by 10 km/h, it would have taken 3 hours more than the scheduled time.
(x - 10)(t + 3) = xt
xt + 3x - 10t - 30 = xt
3x -10t = 30 ....(2)
Adding equations (1) and (2), we obtain
- 2x + 10t + 3x -10t = 20 + 30
x = 50
Substituting x = 50 in equation (1), we obtain
- 2 × 50 + 10t = 20
- 100 + 10t = 20
10t = 120
t = 120/10
t = 12
Therefore, distance = xt = 50 × 12 = 600
Hence, the distance covered by the train is 600 km.
☛ Check: Class 10 Maths NCERT Solutions Chapter 3
Video Solution:
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
Class 10 Maths NCERT Solutions Chapter 3 Exercise 3.7 Question 3
Summary:
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. The distance covered by the train is 600 km.
☛ Related Questions:
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- Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.
- Solve the following pair of linear equations. (i) px + qy = p - q; qx - py = p + q (ii) ax + by = c; bx + ay = 1+ c (iii) x/a - y/b = 0; ax + by = a² + b² (iv) (a - b)x + (a + b) y = a² - 2ab - b²; (a + b)(x + y) = a² + b² (v) 152x - 378y = -74; - 378x + 152y = - 604
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