Question

) a train travels a distance of 192 km at an average speed of 80 km/h from station p to another station q. It then travels back to p taking 5 hours 36 min. Find the average speed of the train on the return journey to p.

Answer 1

Answer:

525km in 5 hours

Explanation:

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Given:

Speed of first train while travelling from P to Q = 126 km/hr

Speed of first train while travelling from Q to P = 90 km/hr

Another train travels with the average speed of first train.

Distance to be covered by second train = 525 km

Formula used:

Time = Distance/Speed

Average speed = Total Distance/Total time

Calculation:

Let the distance between P and Q be D km

Time taken by first train to travel P to Q = D/126 hours

Time taken by first train to travel Q to P = D/90 hours

Total time taken by first train = D/126 + D/90 = 12D/630

Average speed of first train = Total Distance/Total time

⇒ Average speed of first train = 2D/(12D/630)

⇒ Average speed of first train = 630/6

⇒ Average speed of first train = 105 km/hr

Speed of second train = average speed of first train = 105 km/hr

Time taken by second train = Distance/Speed = 525/105

⇒ Time taken by second train = 5 hours

∴ Time taken by first train to travel 525 km is 5 hours

Alternate method:

Average speed of a train when it travels the same distance with different speed = (2 × S1 × S2)/(S1 + S2)

Where S1 and S2 are speed of the train travelling the same distance.

Average speed of first train = (2 × 126 × 90)/(126 + 90)

⇒ Average speed of first train = 22680/216

⇒ Average speed of first train = 105 km/hr

Speed of second train = average speed of first train = 105 km/hr

Time taken by second train = Distance/Speed = 525/105

⇒ Time taken by second train = 5 hours

∴ Time taken by first train to travel 525 km is 5 hours

Answer 2

Answer:

The correct answer will be -

The train's average speed on the return journey will be 60 km/h.

Explanation:

Given in the question -

• A train travels a distance of 192 km at an average speed of 80 km/h from station P to another station Q.
• It then travels back to P taking 5 hours 36 min.

The total journey from going P to Q and returning to P is = 5 hours 36 min

For the first part - P to Q -

average speed = 80 km/h

total distance = 192 km

total time taken is = $\frac{192}{80} = 2\ hours \ 24\ minutes$

So it will take 2 hours and 24 minutes to reach Q.

For the second part - Q to P -

The time it should take to reach the destination =

$= 5\ hours\ 36 \ min-2\ hours\ 24\ min\\\\= 3\ hours\ 12 \ min = 3.2 \ hours$

Distance = 192 km

The average speed of the train = $\frac{192}{3.2} = 60 \ km/h$

So, the train's average speed on the return journey will be 60 km/h.

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