Calculating Journey Time and Arrival Time

This problem asks us to calculate the time a journey will take and determine the arrival time, given the starting time, distance, and speed. To solve this, we first need to find out how long the journey is expected to last using the relationship between distance, speed, and time.

Understanding the Given Information

• Starting time: 10:45 am
• Speed of journey: 45 km/h
• Distance to destination: 150 km

Calculating the Time Taken for the Journey

The formula relating distance, speed, and time is:

\(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)

Let's plug in the values given in the question:

\(\text{Time} = \frac{150 \text{ km}}{45 \text{ km/h}}\)

Now, we calculate the value:

\(\text{Time} = \frac{150}{45} \text{ hours}\)

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15:

\(\frac{150 \div 15}{45 \div 15} = \frac{10}{3}\)

So, the time taken is \(\frac{10}{3}\) hours.

Converting Hours to Hours and Minutes

The time taken is \(\frac{10}{3}\) hours. This is an improper fraction, which means it is more than 1 hour. Let's convert it to a mixed number to understand it better in terms of hours and a fraction of an hour:

\(\frac{10}{3} = 3 \text{ with a remainder of } 1\)

This means \(\frac{10}{3} \text{ hours} = 3 \frac{1}{3} \text{ hours}\).

So, the journey takes 3 full hours and \(\frac{1}{3}\) of an hour.

To find out how many minutes \(\frac{1}{3}\) of an hour is, we multiply by 60 (since there are 60 minutes in an hour):

\(\frac{1}{3} \text{ hour} = \frac{1}{3} \times 60 \text{ minutes}\)

\(\frac{1}{3} \times 60 = \frac{60}{3} = 20 \text{ minutes}\)

Therefore, the total time taken for the journey is 3 hours and 20 minutes.

Calculating the Arrival Time

Manu started his journey at 10:45 am. The journey duration is 3 hours and 20 minutes. To find the arrival time, we add the journey duration to the starting time:

Start Time: 10:45 am

Journey Duration: + 3 hours 20 minutes

Let's add the hours first:

10:45 am + 3 hours = 1:45 pm

(Since 10 am + 3 hours = 13 hours, which is 1 pm in 12-hour format).

Now, add the minutes:

1:45 pm + 20 minutes

Starting from 1:45 pm, adding 15 minutes gets us to 2:00 pm. We still need to add 20 minutes - 15 minutes = 5 minutes more.

2:00 pm + 5 minutes = 2:05 pm.

So, Manu will reach his destination at 2:05 pm.

The calculation shows that starting at 10:45 am and traveling for 3 hours and 20 minutes results in an arrival time of 2:05 pm.

Revision Table: Time, Speed, Distance

Additional Information on Time Calculations

• When adding time durations, add hours to hours and minutes to minutes separately.
• If the minutes total 60 or more, convert 60 minutes into 1 hour and add it to the hour total.
• Converting between 12-hour (am/pm) and 24-hour formats can be helpful for time calculations, especially across noon or midnight. For example, 10:45 am is 10:45 in 24-hour format. Adding 3 hours gives 13:45, and adding 20 minutes gives 14:05. 14:05 in 24-hour format is 2:05 pm in 12-hour format.
• Ensure that units are consistent. If speed is in km/h and distance in km, time will be in hours. If time is needed in minutes, convert the resulting hour value.