What is the average speed of a truck if it travels 2/3 of a distance between 2 towns at 80 km/h and the remaining distance at 90 km/h?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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The distance between towns, covered by the truck is unknown and we'll note it as x.

We'll split the distance in 2x/3 and x/3, since the truck covers the first part of distance at the v1 speed, of 80 km/h, and the other part at the v2 speed, of 90 km/h.

The first part of distance is covered in the time t1, and the other half in the time t2.

We'll write the formula of speed:

v = x/t (1)

v1 = (2x/3)/t1

We'll substitute v1:

80 = (2x/3)/t1

We'll divide by 2:

40 = x/3t1

t1 = x/120 hour

v2 = (x/3)/t2

We'll substitute v2:

90 = (x/3)/t2

t2 = x/270 hour

Now, we'll write the average speed:

av. v = total distance covered/total time taken

av. v = x/(t1+t2)

We'll substitute t1 and t2:

av. v = x/(x/120+x/270)

av. v = x/(9x+4x)/1080

av. v = 1080x/13x

We'l simplify and we'll get:

av. v = 1080/13

av. v = 83 Km/h approx.

The average speed of the car is av. v = 83 Km/h.