Question

A particle goes from A to B with a speed of 40 km/h and B to C with a speed of 60 km/h. If AB = 6BC, the average speed in km/h between A and C is ____

• A. 42km/h
• B. 50km/h
• C. 60km/h
• D. 40km/h

Answer 1

The correct option is A 42km/h

Gievn,

$AB=6BC$

Total distance, $AC=AB+BC$

$AC=6BC+BC=7BC$

From the above figure,

The time required to covered distance $AB$ is

$t_1=\frac{AB}{40}hr$

$t_1=\frac{6BC}{40}hr$

Time required to covered distance $BC$ is

$t_2=\frac{BC}{60}hr$

Total time, $t=t_1+t_2$

$t=\frac{6BC}{40}+\frac{BC}{60}$

$t=0.1667BChr$

Average speed, $v_{avg}=\frac{Totaltime}{Totaltime}$

$v_{avg}=\frac{AC}{t}$

$v_{avg}=\frac{7BC}{0.1667BC}=\frac{7}{0.1667}$

$v_{avg}=41.99\approx 42km/h$

The correct option is A.