Answer to Question #215511 in Algebra for Naad

Question

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.

Answer 1

Let $AB=BC=CA=x\ km.$

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

On side $AB$ the time will be $t_1=\dfrac{x}{30}\ h.$

On side $BC$ the time will be $t_2=\dfrac{x}{40}\ h.$

On side $CA$ the time will be $t_3=\dfrac{x}{50}\ h.$

The total time of the trip will be

$$t_1+t_2+t_3=\dfrac{x}{30}+\dfrac{x}{40}+\dfrac{x}{50}=\dfrac{47x}{600}$$

The average speed for the entire trip is

$$v_{ave}=\dfrac{3x}{\dfrac{47x}{600}}=\dfrac{1800}{47} (km/h)\approx38.298\ km/h$$