Question

A man makes a trip by automobile at an average speed of 50 km/hr. He returns over the same route at an average speed of 45 km/hr. His average speed for the entire trip is:

• A. $47\frac{7}{19}$
• B. $47\frac{1}{4}$
• C. $47\frac{1}{2}$
• D. $47\frac{11}{19}$
• E. none of these

Answer 1

The correct option is A $47\frac{7}{19}$

Let distance be $x$

speed in $1^{st}$ trip $=50km/hr.$

$\therefore$ Time taken $\frac{x}{50}hrs.$

speed in return trip $=45km/hr$

$\therefore$ Time taken $=\frac{x}{45}hrs.$

Avg. speed $=\frac{TotalDistance}{Totaltime}$

$=\frac{x+x}{x/50+x/45}$

$=\frac{2x\times 45\times 50}{45x+50x}$

$=\frac{2\times 50\times 45}{95}=\frac{4500}{95}$

$=\frac{900}{19}=47\frac{7}{19}$