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Jose drove to the mountains last weekend. There was heavy traffic on the way there, the trip took eight hours. When jose drove home, there was no traffic and the trip only took five hours. If his average rate was 21 mph faster on the trip home, how far away does jose live from the mountains

Sagot :

MrRoyal

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

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