John drives his car from home to university at an average speed of 30 km/h and increases his speed by 10km/h every 10 minutes. What is the distance covered in 30 minutes? Please explain step by step and clearly.
break the drive into three units of speed.
a. avg speed=30, distance =30*10/60=5km
b. avg speed=40,distance=40*10/60=6.66km
c. avg speed=50, distance=50*10/60=8.33km
add the distances for the units=total distance
Thanks
To find the total distance covered by John in 30 minutes, we need to break down the problem into smaller time intervals and calculate the distance traveled during each interval.
Given:
- Average speed: 30 km/h
- Increase in speed: 10 km/h every 10 minutes
First, let's determine how many intervals of 10 minutes are there in 30 minutes.
30 minutes / 10 minutes = 3 intervals
Next, let's calculate the distance John covers during each interval.
Interval 1 (0-10 minutes):
- Speed: 30 km/h
- Time: 10 minutes
- Distance covered: Speed * Time = 30 km/h * 10 minutes = 300 km
Interval 2 (10-20 minutes):
- Speed: 30 km/h + 10 km/h (increase)
- Time: 10 minutes
- Distance covered: Speed * Time = (30 km/h + 10 km/h) * 10 minutes = 40 km/h * 10 minutes = 400 km
Interval 3 (20-30 minutes):
- Speed: 30 km/h + 10 km/h (increase)
- Time: 10 minutes
- Distance covered: Speed * Time = (30 km/h + 2 * 10 km/h) * 10 minutes = 50 km/h * 10 minutes = 500 km
Now, we sum up the distances covered during each interval to find the total distance covered in 30 minutes.
Total distance = Distance in interval 1 + Distance in interval 2 + Distance in interval 3
= 300 km + 400 km + 500 km
= 1200 km
Therefore, John covers a distance of 1200 kilometers in 30 minutes.