Question

1. A man walks at a speed of 6 km/hr for 1 km and 8 km/hr
for the next 1 km. What is his average speed for the walk
of 2 km ?​

Answer 1

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✦ Required Answer:

♦️ GiveN:

• First he walks 1 km with speed 6 km/hr
• Then, he walks 1 km with speed 8 km/hr.

♦️To FinD:

• Average speed for entire journey...?

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✦Explanation of Concept:

Before solving this question, we need to know the concept of average speed, here it is:

♠️ Average speed:

As we know that, speed is the rate of distance covered or distance travelled in the given time interval. As the name says, average speed is the total distance by total time taken.

$\large{ \dag{ \boxed{ \rm{ \pink{Avg. \: speed = \frac{Total \: distance}{Total \: time \: taken} }}}}}$

We always have to keep in mind, that to find the average speed, we should have the total distance and total time.

Also we gonna use the simple formula of speed,

$\large{ \dag{ \boxed{ \rm{ \pink{Speed = \frac{Distance}{Time} }}}}}$

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✦Solution:

Given, distance travelled = 1 km

Speed of the body = 6 km/hr

So, we can easily find the time, by using the simple speed,distance and time formula,

By using formula,

$\large{ \rm{ \dashrightarrow Speed = \frac{Distance}{Time} }} \\ \\ \large{ \rm{ \dashrightarrow \: 6 \: km {h}^{ - 1} = \frac{1 \: km}{time}}} \\ \\ \large{ \rm{ \dashrightarrow \: Time = \frac{1 \: km}{6 \: km {h}^{ - 1} }}} \\ \\ \large{ \rm{ \dashrightarrow \: Time = \frac{1}{6} hr}}$

Now, the body covers 1 km with speed 8 km/hr, again we can use formula,

By using formula,

$\large{ \rm{ \dashrightarrow \: Time = \frac{1 \: km}{8 \: km {h}^{ - 1} } }} \\ \\ \large{ \rm{ \dashrightarrow \: Time = \frac{1}{8} hr}}$

Now, as we have total distance and total time, we would apply the avg. speed formula, to find the answer.

By using formula,

$\large{ \rm{ \dashrightarrow \: Avg. \: speed = \frac{Total \: distance}{Total \: time \: taken}}} \\ \\ \large{ \rm{ \dashrightarrow \: Avg. \: speed = \frac{1 \: km + 1 \: km}{ \frac{1}{6}hr + \frac{1}{8} hr }}} \\ \\ \large{ \rm{ \dashrightarrow \: Avg. \: speed = \frac{2 \: km}{ \frac{4 + 3}{24}hr } }} \\ \\ \large{ \rm{ \dashrightarrow \: Avg. \: speed = \frac{2 \times 24}{7} km {h}^{ - 1}}} \\ \\ \large{ \rm{ \dashrightarrow \: Avg. \: speed = \frac{48}{7} km {h}^{ - 1}}} \\ \\ \large{ \rm{ \dashrightarrow \: Avg. \: speed = \boxed{ \rm{ \green{6.85 \: km {h}^{ - 1} }}}}} \\ \\ \large{ \therefore{ \rm{ \underline{ \underline{ \purple{Hence, \: solved \: \dag}}}}}}$

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