A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed
Solution:
We have to find the original average speed of the train.
Total journey completed in 3 hours.
We know, distance = speed/time
Given, a train travels a distance of 63km at an average speed of x km/hr,
Time = 63/x
Given, same train travels a distance of 72km at an average speed of (x+6)km/hr,
Time = 72/(x+6)
So, 3 = (63/x) + 72/(x+6)
Dividing by 3 on both sides,
1 = 21/x + 24/(x+6)
x(x + 6) = 21(x + 6) + 24(x)
x² + 6x = 21x + 126 + 24x
By grouping,
x² + 6x - 21x - 24x = 126
x² - 39x - 126 = 0
x² - 42x + 3x - 126 = 0
x(x - 42) + 3(x - 42) = 0
(x - 42)(x + 3) = 0
Now, x - 42 = 0
x = 42
Also, x + 3 = 0
x = -3
Since the average speed x cannot be negative, x = 42km/hr
Therefore, the original average speed of the train is 42km/hr.
✦ Try This: A train travels at a certain average speed for a distance of 37 km and then travels a distance of 32km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.4 Sample Problem 3
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed
Summary:
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, its original average speed is 42 km/hr
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