This is a problem number 3 from TOMATO based on Calculating Average Speed.
Problem: Calculating Average Speed.
A boy walks from his home to school at 6 kmph. He walks back at 2 kmph. His average speed, in kmph is
(A) 3; (B) 4; (C) 5; (D) $\sqrt {12}$;
Discussion:
Suppose the distance from home to school is t km.
Time taken for home to school journey: $\frac {t}{6}$
Time taken for school to home journey: $\frac {t}{2}$
Hence average speed = $\frac {distance}{time} = \frac {2t}{\frac{t}{6} + \frac{t}{2}} = 3$
There fore average speed is 3 kmph.
Note that it is the harmonic mean of the two given speeds instead of arithmetic mean.
This is a problem number 3 from TOMATO based on Calculating Average Speed.
Problem: Calculating Average Speed.
A boy walks from his home to school at 6 kmph. He walks back at 2 kmph. His average speed, in kmph is
(A) 3; (B) 4; (C) 5; (D) $\sqrt {12}$;
Discussion:
Suppose the distance from home to school is t km.
Time taken for home to school journey: $\frac {t}{6}$
Time taken for school to home journey: $\frac {t}{2}$
Hence average speed = $\frac {distance}{time} = \frac {2t}{\frac{t}{6} + \frac{t}{2}} = 3$
There fore average speed is 3 kmph.
Note that it is the harmonic mean of the two given speeds instead of arithmetic mean.