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The distance between the 2 cities is 225 kilometers. a passenger car and a truck drove from the two cities at the same time. they met after 2.5 hours. the speed ratio of the truck to the passenger car is known to be 4:5. how many kilometers per hour does the truck travel

Sagot :

xero099

The truck travels at a velocity of 360 kilometers per hour.

Let suppose that both the passenger car and the truck travel at constant velocity, we have following formula if they meet each other at a given point:

System of equations

Passenger car

[tex]x = v_{P}\cdot t[/tex] (1)

Truck

[tex]L-x = v_{T}\cdot t[/tex] (2)

Velocity Ratio

[tex]\frac{v_{T}}{v_{P}} = r[/tex] (3)

Where:

  • [tex]x[/tex] - Distance travelled by the passenger car, in kilometers.
  • [tex]L[/tex] - Distance between the two cities, in kilometers.
  • [tex]v_{P}[/tex] - Velocity of the passenger car, in kilometers per hour.
  • [tex]v_{T}[/tex] - Velocity of the truck, in kilometers per hour.
  • [tex]t[/tex] - Time, in hours.

Now we proceed to reduce the system of linear equations:

(1) and (3) in (2):

[tex]L - v_{P}\cdot t = v_{P}\cdot r \cdot t[/tex]

[tex]L = v_{P}\cdot (1-r)\cdot t[/tex]

[tex]v_{P} = \frac{L}{(1-r)\cdot t}[/tex] (4)

And by (3) and (4) we know the velocity of the truck:

[tex]v_{T} = \frac{r\cdot L}{(1-r)\cdot t}[/tex]

If we know that [tex]r = \frac{4}{5}[/tex], [tex]L = 225\,km[/tex] and [tex]t = 2.5\,h[/tex], then the velocity of the truck is:

[tex]v_{T} = \frac{\left(\frac{4}{5} \right)\cdot (225\,km)}{\left(1-\frac{4}{5} \right)\cdot (2.5\,h)}[/tex]

[tex]v_{T} = 360\,\frac{km}{h}[/tex] [tex]\blacksquare[/tex]

The truck travels at a velocity of 360 kilometers per hour.

To learn more on systems of linear equations, we kindly invite to know this verified question: https://brainly.com/question/20379472

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