Respuesta :
Answer:
- Trip to work has rate: 24 mph
- Trip back to home has rate: 18 mph
- Distance to work is: 480 m
Step-by-step explanation:
We know that speed is defined as the ratio of distance to time.
i.e.
[tex]Speed=\dfrac{Distance}{Time}[/tex]
Let the distance traveled to work be: x m.
Now, while going to work it takes a person 20 minutes.
This means that the speed of the person while going to work is:
[tex]S_1=\dfrac{x}{20}[/tex]
Also, the time taken to come back home is: 30 minutes.
This means that the speed of person while riding to home is:
[tex]S_2=\dfrac{x}{30}[/tex]
Also, it is given that the rate back is 8 mph slower than the trip to work.
This means that:
[tex]S_1-S_2=8[/tex]
i.e.
[tex]\dfrac{x}{20}-\dfrac{x}{30}=8\\\\i.e.\\\\\dfrac{30x-20x}{600}=8\\\\i.e.\\\\\dfrac{10x}{600}=8\\\\i.e.\\\\\dfrac{x}{60}=8\\\\i.e.\\\\x=480\ \text{m}[/tex]
Hence, the distance to work is: 480 m.
Also, the rate while going to work is:
[tex]=\dfrac{480}{20}\\\\=24\ \text{mph}[/tex]
and the trip back to home is covered with the speed:
[tex]=\dfrac{480}{30}\\\\=16\ \text{mph}[/tex]
