На перегоне длина которого равна 240 км, поезд шел со скоростью на 10 км/ч меньшей, чем должна быть по расписанию опоздал на 48 мин.С какой скоростью должен был идти поезд по расписанию?

Let's assume that the scheduled speed of the train is x km/h.

The train travels a distance of 240 km, so the actual travel time at a speed of (x - 10) km/h is given by the equation:

240 / (x - 10)

Since the train is late by 48 minutes, or 48/60 hours, the actual travel time can be expressed as:

240 / (x - 10) = (240 / x) + 48/60

To simplify the equation, let's convert the minutes to hours:

48/60 = 4/5 hours

240 / (x - 10) = (240 / x) + 4/5

To combine the fractions, let's find a common denominator:

240 / (x - 10) = (240 / x) + (4/5) * (x / x)

240 / (x - 10) = (240 / x) + 4x / (5x)

To simplify the equation further, let's clear the fractions by multiplying through by x(x - 10):

240x = 240(x - 10) + 4x(x - 10) / 5

240x = 240x - 2400 + (4x^2 - 40x) / 5

Multiplying through by 5 to simplify the equation:

1200x = 1200x - 12000 + 4x^2 - 40x

Rearranging the equation to isolate the terms:

4x^2 - 40x = -12000

Dividing through by 4 to simplify:

x^2 - 10x = -3000

Moving all terms to one side to form a quadratic equation:

x^2 - 10x + 3000 = 0

This quadratic equation can be factored as:

(x - 60)(x - 50) = 0

Setting each factor equal to zero:

x - 60 = 0 or x - 50 = 0

Solving for x:

x = 60 or x = 50

Since the train cannot travel at a speed of 60 km/h and be late, the scheduled speed of the train should be 50 km/h.