Respuesta :
Answer:time taken to run from his house to the park is 12 minutes
Step-by-step explanation:
Let x represent the distance between his house and the park.
The speed at which Adrian ran from his house to the park is 5 meters per second.
Distance = speed × time
Time = distance/speed
Therefore, time taken to run from his house to the park would be
Time = x/5
The speed at which he ran back from the park to his house is 6 meters per second.
Time taken to run back from the park to his house would be
Time = x/6
The total time taken to run the whole journey was 22 minutes. Converting to seconds, it becomes 22× 60 = 1320 seconds. Therefore,
x/5 + x/6 = 1320
Multiplying through by 30, it becomes
6x + 5x = 39600
11x = 39600
x = 39600/11 = 3600 meters
Therefore, time taken to run from his house to the park would be
x/5 = 3600/5 = 720 seconds
Converting to minutes, it becomes
720/60 = 12 minutes
The time taken from Adrian's house to the park is 12 minutes.
Speed, distance, and Time
We know that sped, distance, and time all are in a relationship to each other. this relationship can be given as,
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given to us,
- Adrian speed from his house to the park = 5 meters/speed,
- Adrian speed from the park to his house = 6 meters/speed,
- The total time is taken to run the whole journey = 22 minutes,
Distance
As we know that the distance from Adrian's house to the park and the distance from the park to Adrian's house will be the same.
Time
Let the time needed to travel from the house to the park be x, then the time needed to travel from the park to the house be (22-x).
Therefore,
Distance from Adrian's house to the park
= distance from the park to Adrian's house
[tex]5 \times x = 6 \times (22-x)\\5x = 132 - 6x\\5x + 6x = 132\\11x = 132\\x = \dfrac{132}{11}\\x = 12\ minutes[/tex]
Hence, the time taken from Adrian's house to the park is 12 minutes.
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