Question

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

Answer 1

EXPLANATION.

Case = 1.

=> Train travels the first 15 km at a uniform

speed of 30 km/hr.

$\sf : \implies \: speed \: \: = \dfrac{distance}{time} \\ \\ \sf : \implies \: time \: = \frac{distance}{speed} \\ \\ \sf : \implies \: t_{1} = \cancel{\frac{15}{30}} = \frac{1}{2}$

Case = 2.

next 75 km at uniform speed of 50 km/hr.

$\sf : \implies \: t_{2} = \cancel{\dfrac{75}{50}} = \dfrac{3}{2}$

Case = 3.

Last 10 km at a uniform speed of 20 km/hr.

$\sf : \implies \: t_{3} = \cancel{\dfrac{10}{20}} = \dfrac{1}{2}$

Total distance = 15 + 75 + 10 = 100 km.

Total time taken

$\sf : \implies \: \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{3}{2} = \dfrac{5}{2}$

$\sf : \implies \: average \: speed \: = \dfrac{total \: distance \: covered}{total \: time \: taken} \\ \\ \sf : \implies \: \frac{100}{ \frac{5}{2} } = \frac{200}{5} = 40 \: km \: hr {}^{ - 1}$

Answer 2

Answer:

✡ Given ✡

$\leadsto$ A train travels the first 15 km at a uniform speed of 30 km/h .

$\leadsto$ The next 75 km at a uniform speed of 50 km/h.

$\leadsto$ The last 10 km at a uniform speed of 20 km/h.

✡ To Find ✡

$\leadsto$ What is the average speed for the entire journey.

✡ Solution ✡

Given,

➡ $\sf{d_1}$ = 15 km, $\sf{v_1}$ = 30 km/h

➡ $\sf{d_2}$ = 75 km, $\sf{v_2}$ = 50 km/h

➡ $\sf{d_3}$ = 10 km, $\sf{v_3}$ = 20 km/h

We know that,

✳ Average speed = $\dfrac{total\: distance\: covered}{total\: time\: taken}$

▶ Total distance covered = D

$\implies$ 15+75+10 = 100 km

▶ Total time taken = T

$\implies$ ($\dfrac{15}{30}$) + ($\dfrac{75}{50}$) + ($\dfrac{10}{20}$) = 2.5 hrs

So, average speed ,

$\implies$ $\dfrac{100}{2.5}$ = $\text{\large\underline{\pink{40 km/h}}}$

Hence, the average speed for the entire journey is 40 km/h

Step-by-step explanation:

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