Question

1/3 of a certain journey is covered at the rate of 25 km/h , 1/4 at the rate of 30 km/h and the rest of 50 km/h.What is the average speed for the
whole journey?

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Answer 1

Answer :

Average speed for the journey = 33.33 km / hour

Solution with detailed explanation :

Let the total distance be x km .

For first part ,

Time = $\sf\dfrac{Distance}{Speed}$

( $\sf\dfrac{1}{3}$ of x = $\sf\dfrac{x}{3}$ and speed = 25 km / hour )

Time = $\sf\dfrac{\frac{x}{3}}{25}$

• $\sf\dfrac{x}{25\:\times\:3}$

• $\sf\dfrac{x}{75}\:hours$

For second part ,

Time = $\sf\dfrac{Distance}{Speed}$

( $\sf\dfrac{1}{4}$ of x = $\sf\dfrac{x}{4}$ and speed = 30 km / hour )

Time = $\sf\dfrac{\frac{x}{4}}{30}$

$\sf\dfrac{x}{30\:\times\:4}$

$\sf\dfrac{x}{120}\:hours$

For third part ,

Remaining distance would be x - ( 1/3 rd part + 1/4th part )

• x - ( $\sf\dfrac{x}{4}$ + $\sf\dfrac{x}{3}$

• x - $\sf\dfrac{7x}{12}$

Cross multiply

• $\sf\dfrac{12x\:-\:7x}{12}$

• $\sf\dfrac{5x}{12}\:km$

Time = $\sf\dfrac{\frac{5x}{12}}{50}$

$\sf\dfrac{5x}{50\:\times\:12}$

$\sf\dfrac{5x}{600}\:hours$

Average speed = $\sf\dfrac{Total\: distance\:covered}{Total\:time\:taken}$

• $\sf\dfrac{x}{\frac{x}{75}\:+\:\frac{x}{120}\:+\:\frac{5x}{600}}$

• $\sf\dfrac{x}{\frac{8x\:+\:5x\:+5x}{600}}$

• $\sf\dfrac{x}{\frac{18x}{600}}$

• $\sf\dfrac{600x}{18x}$

• 33.33 km / hour

Answer 2

Answer:

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