Three students travel a distance of 60 km at a speed of 12 km per hour 15 km per hour, and 20 km per hour, respectively starting together on one set of axes draw graphs to show the positions at any time we find the time that each one takes to travel 24 km show full working in all.
To solve this problem, we can use the formula:
Distance = Speed × Time
For the first student traveling at a speed of 12 km/h, we have:
Time1 = Distance / Speed1
Time1 = 24 km / 12 km/h
Time1 = 2 hours
So, the first student takes 2 hours to travel 24 km.
For the second student traveling at a speed of 15 km/h, we have:
Time2 = Distance / Speed2
Time2 = 24 km / 15 km/h
Time2 = 1.6 hours
However, since time cannot be represented as a fraction of an hour on the graph, we need to convert 1.6 hours to minutes:
1.6 hours × 60 minutes/hour = 96 minutes
So, the second student takes 1 hour and 36 minutes (or 96 minutes) to travel 24 km.
For the third student traveling at a speed of 20 km/h, we have:
Time3 = Distance / Speed3
Time3 = 24 km / 20 km/h
Time3 = 1.2 hours
However, since time cannot be represented as a fraction of an hour on the graph, we need to convert 1.2 hours to minutes:
1.2 hours × 60 minutes/hour = 72 minutes
So, the third student takes 1 hour and 12 minutes (or 72 minutes) to travel 24 km.
Now, let's draw graphs to represent the positions of the three students at any time:
On the x-axis, we represent time in hours, and on the y-axis, we represent distance in kilometers.
For the first student:
x (time) | y (distance)
-----------------------
0 | 0
1 | 12
2 | 24
3 | 36
4 | 48
5 | 60
For the second student:
x (time) | y (distance)
-----------------------
0 | 0
1 | 15
1.6 | 24
2 | 30
3 | 45
4 | 60
For the third student:
x (time) | y (distance)
-----------------------
0 | 0
1 | 20
1.2 | 24
2 | 40
2.4 | 48
3 | 60
I apologize, but as a text-based AI, I cannot draw graphs on this platform, but I hope you can picture the graphs based on the coordinates provided.