Answer to Question #215511 in Algebra for Naad

Question #215511

Cities A, Band C are equidistant from each other. A motorist travels from A to

B at 30 km/h; from B to C at 40 km/h and from C to A at 50 km/h. Determine

his average speed for the entire trip.


1
Expert's answer
2021-07-11T17:54:22-0400

Let AB=BC=CA=x km.AB=BC=CA=x\ km.

The total distance will be AB+BC+CA=3x.AB+BC+CA=3x.

On side ABAB the time will be t1=x30 h.t_1=\dfrac{x}{30}\ h.


On side BCBC the time will be t2=x40 h.t_2=\dfrac{x}{40}\ h.


On side CACA the time will be t3=x50 h.t_3=\dfrac{x}{50}\ h.

The total time of the trip will be


t1+t2+t3=x30+x40+x50=47x600t_1+t_2+t_3=\dfrac{x}{30}+\dfrac{x}{40}+\dfrac{x}{50}=\dfrac{47x}{600}

The average speed for the entire trip is


vave=3x47x600=180047(km/h)38.298 km/hv_{ave}=\dfrac{3x}{\dfrac{47x}{600}}=\dfrac{1800}{47} (km/h)\approx38.298\ km/h


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