A distance of 150 km is covered by the Satabdi train in 5 hours less than by the Rajdhani train. Find the time taken by the Rajdhani train to cover the whole journey, if the Rajdhani train is 5 km/h slower than the Satabdi train.
Answer (2)
The Rajdhani train takes 15 hours to cover the distance of 150 km. This is calculated after defining the speeds of both the Satabdi and Rajdhani trains and setting up an equation based on the time difference provided. By solving the quadratic equation, we find the speeds and subsequently the time taken.
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To solve this problem, we need to find the time taken by the Rajdhani train to cover a distance of 150 km. Let's break down the problem step by step.
Define Variables:
Let the speed of the Satabdi train be S km/h.
Therefore, the speed of the Rajdhani train is S − 5 km/h because it is 5 km/h slower.
Time Taken by Each Train:
The time taken by the Satabdi train to cover 150 km is S 150 hours.
The time taken by the Rajdhani train is S − 5 150 hours.
Understand the Time Relation:
It's given that the Satabdi train takes 5 hours less than the Rajdhani train.
So, S − 5 150 − S 150 = 5 .
Solve the Equation:
Find a common denominator and solve the equation: S ( S − 5 ) 150 S − 150 ( S − 5 ) = 5
Simplifying the numerator: 150 S − 150 S + 750 = 750
Therefore, S ( S − 5 ) 750 = 5 .
Solve for S : 750 = 5 S ( S − 5 ) 750 = 5 S 2 − 25 S 5 S 2 − 25 S − 750 = 0
Divide the entire equation by 5: S 2 − 5 S − 150 = 0
Factor or use the quadratic formula to solve: S = 2 5 ± 25 + 600 S = 2 5 ± 625 S = 2 5 ± 25
So, S = 15 (since speed must be positive and practical for the situation), the speed of Satabdi is 20 km/h.
Find Rajdhani's Time:
Now the speed of Rajdhani is 20 − 5 = 15 km/h.
Time taken by Rajdhani is 15 150 = 10 hours.
Thus, the time taken by the Rajdhani train to cover the whole journey is 10 hours.
