Answer:
The distance is 280 miles
Step-by-step explanation:
Given
When going to the mountain:
Let the speed be x.
[tex]Speed = x[/tex]
[tex]Time = 8[/tex]
When going home:
[tex]Speed = 21 + x[/tex]
[tex]Time = 5[/tex]
Required
Determine the distance of the mountains
Distance is calculated as:
[tex]Distance = Speed * Time[/tex]
When going to the mountains, the distance is:
[tex]Distance = x * 8[/tex]
When going home, the distance is:
[tex]Distance = (21 + x) * 5[/tex]
It should be noted that, the distance is the same.
So, we have:
[tex]x * 8 = (21 + x) * 5[/tex]
Open bracket
[tex]x * 8 = 21* 5 + x * 5[/tex]
[tex]8x = 105 + 5x[/tex]
Collect Like Terms
[tex]8x - 5x= 105[/tex]
[tex]3x= 105[/tex]
Divide both sides by 3
[tex]x= \frac{105}{3}[/tex]
[tex]x= 35[/tex]
Substitute 35 for x in
[tex]Distance = x * 8[/tex]
[tex]Distance = 35 * 8[/tex]
[tex]Distance = 280[/tex]
The distance is 280 miles
