Cars overtaking:
Sara left Kootenay National Park at 08:00 and drove toward Vancouver at 85 km/h. Allana left the park an hour later and drove along the same route at 100 km/h. At what time did Allana overtake Sara?
Sara had an 85 km head start
Allana left an hour after Sara and closed the gap at 15 kph
time needed to overtake ... 85 km / 15 kph
To find out when Allana overtakes Sara, we need to determine the distance that Sara traveled before Allana caught up to her.
Given:
- Sara's speed = 85 km/h
- Allana's speed = 100 km/h
- Allana left one hour later than Sara
By the time Allana starts her journey, Sara has already been driving for one hour. Therefore, we need to calculate the distance that Sara covers in that one hour.
Distance covered by Sara in one hour = speed * time
Distance = 85 km/h * 1 hour = 85 km
Now, we know that Allana's speed is greater than Sara's (100 km/h versus 85 km/h), so she will eventually catch up to Sara.
The time it takes for Allana to catch up to Sara can be calculated using the equation:
Time = distance / relative speed
Relative speed = Allana's speed - Sara's speed = 100 km/h - 85 km/h = 15 km/h
Time = 85 km / 15 km/h = 5.67 hours (rounded to 2 decimal places)
Now, we need to convert the time into hours and minutes. Since Allana started an hour later than Sara (due to Sara's one-hour head start), we need to add this extra hour to the time it took for Allana to catch up to Sara.
Total time taken = 5.67 hours + 1 hour = 6.67 hours (rounded to 2 decimal places)
To convert this into minutes, multiply the decimal part (0.67) by 60:
0.67 * 60 = 40.2 minutes (rounded to the nearest minute)
Therefore, Allana overtakes Sara approximately 6 hours and 40 minutes after she starts her journey.
To find out the time Allana overtakes Sara, we add this time to the time Allana started:
Allana overtakes Sara at 08:00 + 6 hours and 40 minutes = 14:40 (2:40 PM)
So, Allana overtakes Sara at approximately 2:40 PM.
To determine at what time Allana overtakes Sara, we need to calculate the time it takes for Allana's car to catch up to Sara's car.
Let's first calculate the head start Sara had by the time Allana started driving. Sara left at 08:00 and Allana left an hour later, so the head start time for Sara is 1 hour.
Next, we need to determine the distance traveled by Sara during that head start time. Since Sara's speed is 85 km/h and she drove for 1 hour, the distance traveled is:
Distance = Speed * Time = 85 km/h * 1 hour = 85 km.
Now, since Allana's speed is 100 km/h, and she needs to catch up with Sara's head start distance of 85 km, we can calculate the time it will take for Allana to catch up to Sara.
Time = Distance / Speed = 85 km / 100 km/h = 0.85 hours.
Therefore, it will take Allana 0.85 hours to catch up to Sara.
To find out the time when Allana overtakes Sara, we need to add this time to Allana's departure time. Allana left one hour after Sara, so her departure time is 09:00.
Time of Allana overtaking Sara = Allana's departure time + Time taken to catch up = 09:00 + 0.85 hours.
Converting the time from a decimal to minutes, 0.85 hours is equal to 0.85 * 60 = 51 minutes.
Therefore, Allana overtakes Sara at 09:00 + 51 minutes = 09:51.
So, Allana overtakes Sara at 09:51.