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A train left Richmond at 6:42 am and arrived at Central Station at 8:04 am - HSC - SSCE Mathematics Standard - Question 11 - 2024 - Paper 1

Question 11

A train left Richmond at 6:42 am and arrived at Central Station at 8:04 am. The distance travelled by the train from Richmond to Central was 61 km. What was the ave... show full transcript

Worked Solution & Example Answer:A train left Richmond at 6:42 am and arrived at Central Station at 8:04 am - HSC - SSCE Mathematics Standard - Question 11 - 2024 - Paper 1

Step 1

Calculate the Time Taken for the Journey

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Answer

The train left Richmond at 6:42 am and arrived at 8:04 am.

To find the time taken, we first convert both times to minutes:

Departure: 6 hours × 60 minutes/hour + 42 minutes = 402 minutes
Arrival: 8 hours × 60 minutes/hour + 4 minutes = 484 minutes

Now, we calculate the time taken:

Time taken (in minutes) = Arrival time - Departure time = 484 minutes - 402 minutes = 82 minutes.

Step 2

Convert Time to Hours

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Next, convert the time taken from minutes to hours:

Time taken (in hours) = rac{82 ext{ minutes}}{60 ext{ minutes/hour}} ext{ = } rac{82}{60} ext{ = } 1.3667 ext{ hours (approximately)}.

Step 3

Calculate the Average Speed

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We can now calculate the average speed using the formula:

Average speed = rac{ ext{Distance}}{ ext{Time}} = rac{61 ext{ km}}{1.3667 ext{ hours}} ext{ = } 44.7 ext{ km/h (approximately)}.

Finally, rounding to the nearest km/h gives us an average speed of 45 km/h.

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