The train made an emergency stop for 24 minutes. By increasing its speed by 10 km / h

The train made an emergency stop for 24 minutes. By increasing its speed by 10 km / h, it will make up for lost time on the 80 km journey. How fast did the train travel along the way?

In this task, we need to find the initial speed of the train. Since we do not know it, we will designate it by “X”. To simplify the calculations, let’s convert 24 minutes into hours, dividing 24 by 60, we get 2/5 or 0.4 hours. Next, we will consider two components of time to form an equation: 1) if the train did not stop, then the time is equal to 80 / X hours; 2) if the train stopped for 0.4 hours, then the time to overcome 80 km of track will be equal to 80 / (X + 10). Now let’s make the equation: 80 / X = (80 / (X + 10)) + 0.4. Having got rid of the numerators in fractions, we get the quadratic equation 0.4X ^ 2 + 4X – 800 = 0. The equation has two roots negative (-40) and positive (50). Since the speed cannot be negative, the correct answer is 50 km / h.
Answer: train speed is 50 km / h.