Respuesta :
Answer:
18 km
Explanation:
Let 'd' be the distance between his house and office.
Normal time taken to reach the office = 'x' hours.
If speed is 24 km/h, time is increased by 5 minutes.
If speed is 30 km/h, time is reduced by 4 minutes.
We know that,
Time taken = Distance traveled ÷ Speed
So, when speed is 24 km/hr, time is increased by 5 minutes.
[tex]1\ min = \frac{1}{60}\ h\\5\ min =\frac{5}{60}=\frac{1}{12}\ h[/tex]
So, time is [tex]x+\frac{1}{12}[/tex]
Therefore,
[tex]x+\frac{1}{12}=\frac{d}{24}\\\\x=\frac{d}{24}-\frac{1}{12}\\\\x=\frac{1}{12}(\frac{d}{2}-1)---------1[/tex]
Now, when speed is 30 km/h, time is reduced by 4 minutes or [tex]\frac{4}{60}=\frac{1}{15}\ hours[/tex]
So, time now is [tex]x-\frac{1}{15}[/tex]
Again using the time formula, we have
[tex]x-\frac{1}{15}=\frac{d}{30}\\\\x=\frac{d}{30}+\frac{1}{15}\\\\x=\frac{1}{15}(\frac{d}{2}+1)-------------2[/tex]
Equations (1) and (2) are equal. So,
[tex]\frac{1}{12}(\frac{d}{2}-1)=\frac{1}{15}(\frac{d}{2}+1)\\\\\frac{15}{12}(\frac{d}{2}-1)=\frac{d}{2}+1\\\\\frac{5d}{8}-\frac{5}{4}=\frac{d}{2}+1\\\\\frac{5d}{8}-\frac{d}{2}=1+\frac{5}{4}\\\\\frac{5d-4d}{8}=\frac{4+5}{4}\\\\\frac{d}{8}=\frac{9}{4}\\\\d=\frac{9\times 8}{4}=\frac{72}{4}=18\ km[/tex]
Therefore, the office is 18 km from his house.
