A person takes a trip, driving with a constant speed of 93.5 km/h except for a 21.0 min rest stop. If the person's average speed is 69.8 km/h, how much time is spent on the trip and how far does the person travel?
To solve this problem, we can use the formula:
Average Speed = Total Distance / Total Time
Given that the average speed is 69.8 km/h and the person's speed during driving is 93.5 km/h, we can set up the equation:
69.8 km/h = Total Distance / Total Time
Let's solve for Total Time first.
Total Time = Total Driving Time + Rest Stop Time
Since the person drove at a constant speed of 93.5 km/h, the total driving time can be calculated using the equation:
Total Driving Time = Distance Traveled / Driving Speed
Now, let's solve for Distance Traveled.
Distance Traveled = Total Driving Time x Driving Speed
We know that Total Driving Time = Total Time - Rest Stop Time. Substituting this into the equation, we get:
Distance Traveled = (Total Time - Rest Stop Time) x Driving Speed
Since the total time spent on the trip includes the rest stop time, we can write:
Total Time = Driving Time + Rest Stop Time
Substituting this into the equation above, we get:
Distance Traveled = (Driving Time) x Driving Speed
From the given information in the problem, we know that the rest stop took 21.0 minutes and the person's speed during driving was 93.5 km/h.Let's calculate the total time on the trip and the distance traveled step by step:
Step 1: Convert rest stop time to hours
Rest Stop Time (in hours) = 21.0 minutes / 60 minutes/hour
Rest Stop Time (in hours) = 0.35 hours
Step 2: Calculate Driving Time
Since the rest stop time is already in hours, the driving time can be calculated as:
Driving Time = Total Time - Rest Stop Time
Step 3: Calculate Total Time
From the problem statement, it is given that the average speed is 69.8 km/h and the driving speed is 93.5 km/h. We can use the formula:
Average Speed = Total Distance / Total Time
Rearranging the formula, we get:
Total Time = Total Distance / Average Speed
Given that the average speed is 69.8 km/h, we have:
Total Time = Total Distance / 69.8 km/h
Step 4: Calculate Distance Traveled
From the previous steps, we can now calculate the distance traveled using the formula:
Distance Traveled = Driving Time x Driving Speed
Now let's plug in the values:
Distance Traveled = (Driving Time) x Driving Speed
Step 5: Calculate Total Time
Total Time = Total Distance / Average Speed
Step 6: Calculate Distance Traveled
Distance Traveled = Driving Time x Driving Speed
Now let's calculate the values step by step:
Step 1: Convert rest stop time to hours
Rest Stop Time (in hours) = 21.0 minutes / 60 minutes/hour
Rest Stop Time (in hours) = 0.35 hours
Step 2: Calculate Driving Time
Since the rest stop time is already in hours, the driving time can be calculated as:
Driving Time = Total Time - Rest Stop Time
Step 3: Calculate Total Time
From the problem statement, it is given that the average speed is 69.8 km/h and the driving speed is 93.5 km/h. We can use the formula:
Average Speed = Total Distance / Total Time
Rearranging the formula, we get:
Total Time = Total Distance / Average Speed
Given that the average speed is 69.8 km/h, we have:
Total Time = Total Distance / 69.8 km/h
Step 4: Calculate Distance Traveled
From the previous steps, we can now calculate the distance traveled using the formula:
Distance Traveled = Driving Time x Driving Speed
Now let's plug in the values:
Distance Traveled = (Driving Time) x Driving Speed
Step 5: Calculate Total Time
Total Time = Total Distance / Average Speed
Step 6: Calculate Distance Traveled
Distance Traveled = Driving Time x Driving Speed
Now let's calculate the values step by step:
Step 1: Convert rest stop time to hours
Rest Stop Time (in hours) = 21.0 minutes / 60 minutes/hour
Rest Stop Time (in hours) = 0.35 hours
Step 2: Calculate Driving Time
Since the rest stop time is already in hours, the driving time can be calculated as:
Driving Time = Total Time - Rest Stop Time
Step 3: Calculate Total Time
From the problem statement, it is given that the average speed is 69.8 km/h and the driving speed is 93.5 km/h. We can use the formula:
Average Speed = Total Distance / Total Time
Rearranging the formula, we get:
Total Time = Total Distance / Average Speed
Given that the average speed is 69.8 km/h, we have:
Total Time = Total Distance / 69.8 km/h
Step 4: Calculate Distance Traveled
From the previous steps, we can now calculate the distance traveled using the formula:
Distance Traveled = Driving Time x Driving Speed
Now let's plug in the values:
Distance Traveled = (Driving Time) x Driving Speed
To find the time spent on the trip, we need to calculate the total time spent driving and add the rest stop time.
Let's first convert the rest stop time from minutes to hours:
Rest stop time = 21.0 min * (1 hour / 60 min) = 0.35 hours
Now, we can find the total time spent driving by subtracting the rest stop time from the total trip time:
Total time spent driving = Average speed / Constant speed = 69.8 km/h / 93.5 km/h = 0.746 hours
To find the total trip time, we sum the driving time and the rest stop time:
Total trip time = Total time spent driving + Rest stop time = 0.746 hours + 0.35 hours = 1.096 hours
To find the distance traveled, we multiply the average speed by the total trip time:
Distance traveled = Average speed * Total trip time = 69.8 km/h * 1.096 hours = 76.5 km
Therefore, the person spends 1.096 hours (or approximately 1 hour and 6 minutes) on the trip and travels a distance of 76.5 km.