Answer :
Answer:
Explanation:
Part a: Total Distance Travelled by the Object
First, we'll convert the time units from minutes to hours because the speeds are given in km/h.
10 minutes =
10
60
60
10
hours =
1
6
6
1
hours
15 minutes =
15
60
60
15
hours =
1
4
4
1
hours
Next, we'll calculate the distance travelled at each speed.
Distance travelled at 10 km/h for
1
6
6
1
hours:
Distance
1
=
Speed
1
×
Time
1
=
10
km/h
×
1
6
hours
=
10
6
km
=
5
3
km
Distance
1
=Speed
1
×Time
1
=10km/h×
6
1
hours=
6
10
km=
3
5
km
Distance travelled at 15 km/h for
1
4
4
1
hours:
Distance
2
=
Speed
2
×
Time
2
=
15
km/h
×
1
4
hours
=
15
4
km
Distance
2
=Speed
2
×Time
2
=15km/h×
4
1
hours=
4
15
km
Total distance travelled is the sum of these distances:
Total Distance
=
Distance
1
+
Distance
2
=
5
3
km
+
15
4
km
Total Distance=Distance
1
+Distance
2
=
3
5
km+
4
15
km
To add these fractions, we find a common denominator (12 in this case):
5
3
=
5
×
4
3
×
4
=
20
12
3
5
=
3×4
5×4
=
12
20
15
4
=
15
×
3
4
×
3
=
45
12
4
15
=
4×3
15×3
=
12
45
Total Distance
=
20
12
+
45
12
=
65
12
km
≈
5.42
km
Total Distance=
12
20
+
12
45
=
12
65
km≈5.42km
Part b: Average Speed of the Object
Average speed is defined as the total distance travelled divided by the total time taken.
Total time taken is the sum of the times for each segment of the trip:
Total Time
=
1
6
hours
+
1
4
hours
Total Time=
6
1
hours+
4
1
hours
To add these fractions, we find a common denominator (12 in this case):
1
6
=
1
×
2
6
×
2
=
2
12
6
1
=
6×2
1×2
=
12
2
1
4
=
1
×
3
4
×
3
=
3
12
4
1
=
4×3
1×3
=
12
3
Total Time
=
2
12
+
3
12
=
5
12
hours
Total Time=
12
2
+
12
3
=
12
5
hours
Average speed is then calculated as:
Average Speed
=
Total Distance
Total Time
=
65
12
km
5
12
hours
=
65
5
km/h
=
13
km/h
Average Speed=
Total Time
Total Distance
=
12
5
hours
12
65
km
=
5
65
km/h=13km/h
Therefore, the answers are:
a) Total distance travelled by the object:
65
12
km
≈
5.42
km
12
65
km≈5.42km
b) Average speed of the object:
13
km/h
13km/h