Question

A train travels along a straight line at a constant speed of 60 mi/h for a distance d and then another distance equal to 2d in the same direction at a constant speed of 80 mi/h. a)What is the average speed of the train for the whole journey?

Answer 1

Given :

• Train travels Distance = d with speed (v1) = 60m/h
• Another distance Travelled by train = 2d with speed (v2) = 80m/h

To Find :

• Average speed

Formula Used :

$\bullet\underline{\boxed{\sf Average \: Speed =\dfrac{Total \: Distance}{Total \: Time}}}$

Solution :

★ Total Time (T)

➞ t = $\dfrac{s}{v}$

➞ t1 = d/60

➞ t2 = 2d/80

➞ t2 = d/40

➞ T = t1 + t2

➞ T = d/60 + d/40

➞ T = $\rm{\dfrac{40d+60d}{60 \times 40}}$

➞ T = $\rm{\dfrac{d}{24}}$

Average Speed = $\rm{\dfrac{Total \: Distance}{Total \; Time}}$

$\implies{\rm \dfrac{d+2d}{\dfrac{d}{24}} }$

$\implies{\rm 3d \times \dfrac{24}{d}}$

$\implies{\bf v_{av}=72 \: m/h }$

Answer :

Average speed of train is 72 m/h