Question

A car travelled from Agra to Jaipur at an average speed of 30 / . On his return journey, his average speed was 45 / . If total time taken is 8.5 hours, find the distance between Agra and Jaipur.​

Answer 1

Answer:

306 km

Step-by-step explanation:

A car travelled from Agra to Jaipur at an average speed of 30 km/h .

On his return journey, his average speed was 45 km/h.

Let the distance from Agra to Jaipur = D

Total time of travel = 8.5 hrs

We have time for entire journey. If we can find average speed for the entire journey, then distance = avg. speed × time.

When same distance is covered in two different speeds, v₁ and v₂, Average speed is given as:

$V_{avg} = \frac{2v_1v_2}{v_1+v_2}\\ \\ \Rightarrow V_{avg} = \frac{2 \times 30 \times 45}{30+45} \\ \\ \Rightarrow V_{avg} = 36 \text{ km/h}$

So Distance between Agra and Jaipur = Vavg × time = 36 × 8.5 = 306 km

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Answer 2

Given:-

• Average speed of car from Agra to Jaipur = 30km/hr
• Average speed of car from Jaipur to Agra = 45km/hr.
• Total time taken by the car for travelling = 8.5 hours.

To find :-

• Distance between Agra and Jaipur.

Solution:-

We have time for entire journey. If we can find average speed for the entire journey, then distance = avg. speed × time.

When same distance is covered in two different speeds, v₁ and v₂, Average speed is given as:

$\large \blue{\underline{ \green{ \boxed{\bf{ \red{ \implies V_{average} = \frac{2V_{1} V_{2}}{ V_{1}+ V_{2}} }}}}}}$

$\large\underline{\bf{ \implies V_{average} = \frac{2×45×30}{45+30} }}$

$\large\underline{\bf{ \implies V_{average} = \frac{2700}{75} }}$

$\large\underline{\bf{ \implies V_{average}= 36}}$

Now we have given a certain time.

So,

$\large\underline{\bf{ \implies36 \times 8.5}}$

$\large\underline{\bf{ \implies306km}}$

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