To determine the time a motorist reached his destination after traveling a distance of 150 km at a speed of 60 km/h, starting at 11:30 a.m., with a 45-minute stop, follow these steps:
### Step 1: Calculate the Travel Time without Stops
1. Distance traveled: 150 km
2. Speed: 60 km/h
First, find the travel time by dividing the distance by the speed:
[tex]\[ \text{Travel time} = \frac{\text{Distance}}{\text{Speed}} = \frac{150 \text{ km}}{60 \text{ km/h}} = 2.5 \text{ hours} \][/tex]
2.5 hours can be broken down into hours and minutes:
[tex]\[ 2.5 \text{ hours} = 2 \text{ hours and } 0.5 \text{ hours} \][/tex]
Since 1 hour = 60 minutes:
[tex]\[ 0.5 \text{ hours} = 0.5 \times 60 \text{ minutes} = 30 \text{ minutes} \][/tex]
So, the travel time is:
[tex]\[ 2 \text{ hours and } 30 \text{ minutes} \][/tex]
### Step 2: Add the Stop Duration to the Travel Time
1. Stop duration: 45 minutes
2. Initial travel time: 2 hours and 30 minutes
Add the stop duration to the travel time:
[tex]\[ 30 \text{ minutes} + 45 \text{ minutes} = 75 \text{ minutes} \][/tex]
Since 75 minutes is more than an hour:
[tex]\[ 75 \text{ minutes} = 60 \text{ minutes} + 15 \text{ minutes} = 1 \text{ hour and } 15 \text{ minutes} \][/tex]
So, total travel time becomes:
[tex]\[ 2 \text{ hours} + 1 \text{ hour} = 3 \text{ hours} \][/tex]
[tex]\[ 30 \text{ minutes} + 15 \text{ minutes} = 45 \text{ minutes} \][/tex]
Thus, the overall travel time is:
[tex]\[ 3 \text{ hours and } 45 \text{ minutes} \][/tex]
### Step 3: Determine the Arrival Time
1. Start time: 11:30 a.m.
2. Total travel time: 3 hours and 45 minutes
Add the travel time to the start time:
[tex]\[ 11:30 \text{ a.m.} + 3 \text{ hours} = 2:30 \text{ p.m.} \][/tex]
Then add the minutes:
[tex]\[ 30 \text{ minutes} + 45 \text{ minutes} = 75 \text{ minutes} \][/tex]
Since 75 minutes is more than an hour:
[tex]\[ 75 \text{ minutes} = 60 \text{ minutes} + 15 \text{ minutes} = 1 \text{ hour and } 15 \text{ minutes} \][/tex]
So, add 1 hour to 2:30 p.m.:
[tex]\[ 2:30 \text{ p.m.} + 1 \text{ hour} = 3:30 \text{ p.m.} \][/tex]
Then add the remaining 15 minutes:
[tex]\[ 3:30 \text{ p.m.} + 15 \text{ minutes} = 3:45 \text{ p.m.} \][/tex]
Therefore, the motorist reached his destination at:
[tex]\[ \boxed{3:45 \text{ p.m.}} \][/tex]
