A person takes a trip, driving with a constant speed of 98.5 km/h except for a 21.0 min rest stop. If the person's average speed is 63.3 km/h, how much time is spent on the trip and how far does the person travel?

How much time in hours and how far in km

distance is not known.

but we know this:
avgspeed*(timedriving+21min)=constantspeed*time

Now I intentionally avoided the difficult part: Change the speed to m/s (from km/hr) and change the time 21min to seconds. You can do other units, but they must be consistent.

To find the time spent on the trip, we need to account for both the driving time and the rest stop. Let's break down the process step-by-step:

1. Driving time: We know that the person's average speed is 63.3 km/h. To find the driving time, we can divide the total distance traveled by the average speed. Let's represent the driving time as Td:

Td = Distance / Average Speed

2. Rest stop time: We are given that there is a 21.0 minute rest stop during the trip.

3. Total trip time: To calculate the total trip time, we need to add the driving time and the rest stop time. Let's represent the total trip time as T:

T = Td + Rest Stop Time

Now, let's calculate the values step-by-step:

1. Calculate the driving time:
We don't have the distance traveled, but we can find it using the average speed and the driving time. Rearranging the formula:

Distance = Average Speed * Driving Time

Therefore:
Driving Time = Distance / Average Speed

2. Since we don't have the distance, we can't find the exact driving time yet.

3. Calculate the total trip time (in hours):
Td is the driving time in hours, and Rest Stop Time is already in minutes. To get the total trip time in hours, we need to convert Rest Stop Time to hours as well. There are 60 minutes in an hour, so:

Rest Stop Time (in hours) = 21.0 minutes / 60 minutes/hour

Now, we can calculate the total trip time:

Total Trip Time = Driving Time + Rest Stop Time (in hours)

4. Calculate Distance:
Now that we have both the driving time and the total trip time, we can find the distance. Rearranging the first formula:

Distance = Average Speed * Driving Time

Plugging in the values we know:

Distance = Average Speed * Total Trip Time (in hours)

By following this process, we can find the time spent on the trip and the distance traveled.