Answer:
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Step-by-step explanation:
To find out how far the dog has run after 2 hours, we can consider the relative speeds of Aaron, Bob, and the dog.
Let's denote:
Aaron's speed as
5
km/h
5km/h
Bob's speed as
7
km/h
7km/h
The dog's speed as
15
km/h
15km/h
Since the dog runs back and forth between Aaron and Bob, it effectively runs at the sum of their speeds. Therefore, the relative speed of the dog with respect to Aaron is
15
km/h
+
5
km/h
=
20
km/h
15km/h+5km/h=20km/h, and with respect to Bob, it is
15
km/h
+
7
km/h
=
22
km/h
15km/h+7km/h=22km/h.
Now, let's calculate the distance each of them covers in 2 hours:
Aaron:
5
km/h
×
2
h
=
10
km
5km/h×2h=10km
Bob:
7
km/h
×
2
h
=
14
km
7km/h×2h=14km
The dog will run for the same duration as Aaron and Bob, so we'll consider the distance covered by the dog when moving towards Aaron and when moving towards Bob.
The distance covered by the dog moving towards Aaron in 2 hours is:
Distance
=
Speed
×
Time
=
20
km/h
×
2
h
=
40
km
Distance=Speed×Time=20km/h×2h=40km
The distance covered by the dog moving towards Bob in 2 hours is:
Distance
=
Speed
×
Time
=
22
km/h
×
2
h
=
44
km
Distance=Speed×Time=22km/h×2h=44km
Now, we add up the distances covered by the dog when moving towards Aaron and when moving towards Bob:
Total distance covered by the dog
=
40
km
+
44
km
=
84
km
Total distance covered by the dog=40km+44km=84km
So, the dog has run a total of
84
84 kilometers after 2 hours.