A train travels 360 km at uniform speed . if the speed had been 5 km / hr more it would have taken 1 hour less for the same journey. find the speed of the train.
pl give me a short cut method to solve.
To solve this problem using a shortcut method, we can use the concept of relative speed. Here's how you can do it:
Let the speed of the train be x km/hr.
According to the given information, if the speed had been 5 km/hr more (x + 5 km/hr), the train would have taken 1 hour less for the same journey.
We know that:
Time = Distance / Speed
So, the time taken to cover 360 km at the original speed x is:
Time1 = 360 / x (equation 1)
And, the time taken to cover the same distance at the increased speed (x + 5) is:
Time2 = 360 / (x + 5) (equation 2)
It is given that the time taken at the increased speed is 1 hour less than the original time:
Time1 - Time2 = 1 (equation 3)
Now, we can substitute the values of Time1 and Time2 from equations 1 and 2 into equation 3:
360 / x - 360 / (x + 5) = 1
To simplify this equation, we can multiply both sides by x(x + 5) to eliminate the fractions:
360(x + 5) - 360x = x(x + 5)
Now, solve this equation to find the value of x. Let me calculate it for you:
360x + 1800 - 360x = x^2 + 5x
1800 = x^2 + 5x
Rearrange the equation to form a quadratic equation:
x^2 + 5x - 1800 = 0
Now, you can solve this quadratic equation by factoring, completing the square, or using the quadratic formula to find the value of x, which represents the speed of the train.
Note: The quadratic equation in this specific problem may not have simple integer solutions, so using the quadratic formula would be the most convenient method to solve it.
since time = distance/speed,
360/x - 1 = 360/(x+5)
Not really a shortcut - just proper setup of what they said.