Question

A train travels 20 km at a uniform speed of 60 km/h and next 20 km at a uniform speed of 80 km/h. What is its average speed?​

Answer 1

we have :-

• uniform speed of train at which it covers 20 km = 60km/h
• in the next 20 km the uniform speed of train = 80 km/h

To find :-

the Average speed of the train.

Formula used :-

$\sf \: time \: = \frac{distance}{speed} \\ \\ \sf \: ave. \: speed \: = \frac{total \: distance \: covered}{total \: time \: taken}$

Solution :-

in first case,

$\sf \: time \: taken \: to \: cover \: 20km \: at \: 60km {h}^{ - 1} \\ \sf \: = \frac{20}{60} = \frac{1}{3} hrs$

in second case,

$\sf \: time \: taken \: to \: cover \: 20km \: at \: 80km {h}^{ - 1} \\ \sf \: = \frac{20}{80} = \frac{1}{4}</strong><strong> </strong><strong>hrs</strong><strong>$

therefore total time taken :-

$= \sf \: \frac{1}{3} + \frac{1}{4} \\ \\ \sf \: = \frac{7}{12}</strong><strong> </strong><strong>hrs</strong><strong>$

total distance covered :-

$\sf \: 20 + 20 \\ \sf= \: 40</strong><strong> </strong><strong>km</strong><strong>$

therefore Ave. speed :-

$\sf \: using \: formula \: we \: get \: \\ \\ \sf \: ave \: speed = \frac{40}{ \frac{7}{12} } \\ \\ \sf = \frac{40 \times 12}{7} \\ \\ \sf = \: \frac{480}{7} \\ \\ \sf = 68.54 \: km \: {h}^{ - 1}$

therefore average speed is 68.54 km/h