A train, travelling at a uniform speed for 360 km, would have taken 48 minutesless to travel the same distance if its speed were 5 km/h more. Find the originalspeed of the train.

Sure, let's solve this step by step.

Step 1: Let's denote the original speed of the train as 'x' km/h.

Step 2: The time taken by the train to cover 360 km at the original speed is 360/x hours.

Step 3: If the speed of the train were 5 km/h more, the speed would be (x+5) km/h. So, the time taken to cover the same distance would be 360/(x+5) hours.

Step 4: According to the problem, the difference in the times taken in both cases is 48 minutes, which is 48/60 = 0.8 hours.

Step 5: So, we can write the equation as 360/x - 360/(x+5) = 0.8.

Step 6: Solving this equation will give us the original speed of the train.

Let's solve it:

Multiply the entire equation by x(x+5) to get rid of the denominators:

360(x+5) - 360x = 0.8x(x+5)

Expanding and simplifying gives:

1800 - 360x = 0.8x^2 + 4x

Rearranging terms gives:

0.8x^2 + 364x - 1800 = 0

To make it easier to solve, let's multiply the entire equation by 10/8 = 1.25:

x^2 + 455x - 2250 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a):

x = [-455 ± sqrt((455)^2 - 41(-2250))] / (2*1) x = [-455 ± sqrt(207025 + 9000)] / 2 x = [-455 ± sqrt(216025)] / 2 x = [-455 ± 465] / 2

We have two possible solutions: x = (465 - 455) / 2 = 5 km/h or x = (-455 - 465) / 2 = -460 km/h.

Since speed cannot be negative, the original speed of the train is 5 km/h.