Question

A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. Calculate the average speed for the entire train journey.

Answer 1

Step 1, Given data

Distance traveled = 15 km, Speed = 30 km/h

Distance traveled = 75 km, Speed = 50 km/h

Distance traveled = 10 km, Speed = 20 km/h

Step 2, Finding the average speed

We know,

$Time=\frac{Distance}{Speed}$

So, For 1st = Time = $\frac{15}{30}$ h

For 2nd = Time = $\frac{75}{50}$ h

For 3rd = Time = $\frac{10}{20}h$

Now,

Average Speed = $\frac{TotalDistance}{Time}$

Or, Average speed = $\frac{15+75+10}{\frac{15}{30}+\frac{75}{50}+\frac{10}{20}}$

Or, Average speed =$\frac{100}{\frac{1}{2}+\frac{3}{2}+\frac{1}{2}}$

After solving

Average speed = 40 km/h