Question

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the speed of the truck.

Answer 1

Answer:

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Step-by-step explanation:

The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:

$t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}$

The sum of these times must be equal to the total time of the trip, therefore:

$t_{stage1} + t_{stage2} = 5$

$\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10$

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.