Question

$\huge{Brainliest\: Question}$
A train runs 25 miles at a speed of 30 mph, another 50 miles at a speed of 40 mph, then due to repairs of the track travels for 6 minutes at a speed of 10 mph and finally covers the remaining distance of 24 miles at a speed of 24 mph. What is the average
speed in miles per hour?​

Answer 1

Given

$\sf\pink{⟶}$ A train runs

• 25 miles at a speed of 30 mph
• 50 miles at a speed of 40 mph
• 24 miles at a speed of 24 mph
• 6 minutes at a speed of 10mph

To find

• Average speed of the train in mph.

Solution

$\sf\green{⟶}$ We have to find the time taken by train to cover the distance given.

★ Using the formula

$\large{\underline{\boxed{\tt{Time = \dfrac{Distance}{Speed}}}}}$

⠀

→ Time taken in covering 25 miles at a speed of 30 mph = $\dfrac{25 × 60}{30}$ minutes

• 50 minutes

→ Time taken in covering 50 miles at a speed of 40 mph = $\dfrac{50 × 60}{40}$ minutes

• 75 minutes

→ Distance covered in 6 minutes at a speed of 10 mph = 1 mile

→ Time taken in covering 24 miles at a speed of 24 mph = $\dfrac{24 × 60}{24}$ minutes

• 60 minutes

⠀

$\sf\pink{⟶}$ Therefore, taking the time taken as weights we have the weighted mean as:

$\begin{tabular}{|c|c|c|}\cline{1-3}Speed\: in\: mph\: (X)& Time\: taken\: (W) & WX \\\cline{1-3}30 & 05 & 1,500 \\\cline{1-3}40& 75& 3,000\\\cline{1-3}10 & 6 & 60\\\cline{1-3}24 & 60 & 1,440\\\cline{1-3}&\sum\limits W = 191&\sum\limits WX = 6.000\\\cline{1-3}\end{tabular}$

★ Formula of weighted mean

$\large{\underline{\boxed{\tt{\bar{X}_W = \dfrac{\sum\limits{WX}}{\sum\limits{W}}}}}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\bar{X}_W = \dfrac{6000}{191}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\bar{X}_W = 31.41}$

⠀

$\bf{\pink{Average\: speed = 31.41\: mph.}}$

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Answer 2

Hope its helps you...!!