A train covers half the distance with a speed of 150km/hr. The remaining part of the distance was covered with a speed of 80 km/hr for half of the time and with the speed of 120km/hr for the other half of the time. For the whole journey, calculate the average distance (in km) covered by the train in one hour.

Correct Option - 1


Detailed Solution:

So, d= 150t₁

t₁ = $\frac{d}{150}$

d = (80+120) t₂

t₂ = $\frac{d}{200}$

Total time = t₁ + 2t₂

$\frac{d}{150}+\frac{2d}{200}$

= $\frac{d}{150}$ + $\frac{d}{100}$

= $\frac{2d+3d}{300}$

$=\frac{5d}{300}=\frac{d}{60}$

Average speed = $\frac{2d}{\frac{d}{60}}$ = 120km/hr.

Average distance covered in one hour is same as average speed.

 

<div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754900341php2WaQJS.jpeg" alt="" width="314" height="100" loading="lazy"></picture></div><div class="figure"><p>So, d= 150t₁</p><p>t₁ =&nbsp;<math><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mn>1</mn><mn>5</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p>d = (80+120) t₂</p><p>t₂ =&nbsp;<math><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mn>2</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p>Total time = t₁ + 2t₂</p><p><math><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mn>1</mn><mn>5</mn><mn>0</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mi>d</mi></mrow><mrow><mn>2</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p>=&nbsp;<math><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mn>1</mn><mn>5</mn><mn>0</mn></mrow></mfrac></mrow></math>&nbsp;+&nbsp;<math><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p>=&nbsp;<math><mrow><mfrac><mrow><mn>2</mn><mi>d</mi><mo>+</mo><mn>3</mn><mi>d</mi></mrow><mrow><mn>3</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p><math><mrow><mo>=</mo><mfrac><mrow><mn>5</mn><mi>d</mi></mrow><mrow><mn>3</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>d</mi></mrow><mrow><mn>6</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p>Average speed =&nbsp;<math><mrow><mfrac><mrow><mn>2</mn><mi>d</mi></mrow><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mn>6</mn><mn>0</mn></mrow></mfrac></mrow></mfrac></mrow></math>&nbsp;= 120km/hr.</p><p>Average distance covered in one hour is same as average speed.</p></div></div><p>&nbsp;</p>

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