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yKpoI14uk [10]
2 years ago
9

Jose drove to the mountains last weekend. There was heavy traffic on the way there, the trip took eight hours. When jose drove h

ome, 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
Mathematics
1 answer:
vodka [1.7K]2 years ago
5 0

Answer:

The distance is 280 miles

<em></em>

Step-by-step explanation:

Given

When going to the mountain:

Let the speed be x.

Speed = x

Time = 8

When going home:

Speed = 21 + x

Time = 5

Required

Determine the distance of the mountains

Distance is calculated as:

Distance =  Speed * Time

When going to the mountains, the distance is:

Distance = x * 8

When going home, the distance is:

Distance = (21 + x) * 5

It should be noted that, the distance is the same.

So, we have:

x * 8 = (21 + x) * 5

Open bracket

x * 8 = 21* 5 + x * 5

8x = 105 + 5x

Collect Like Terms

8x - 5x= 105

3x= 105

Divide both sides by 3

x= \frac{105}{3}

x= 35

Substitute 35 for x in

Distance = x * 8

Distance = 35  * 8

Distance = 280

<em>The distance is 280 miles</em>

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Answer:

  6. (A, B, C) ≈ (112.4°, 29.5°, 38.0°)

  7. (a, b, C) ≈ (180.5, 238.5, 145°)

Step-by-step explanation:

My "work" is to make use of a triangle solver calculator. The results are attached. Triangle solvers are available for phone or tablet and on web sites. Many graphing calculators have triangle solvers built in.

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We suppose you're to make use of the Law of Sines and the Law of Cosines, as applicable.

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The angles (A, B, C) are about (112.4°, 29.5°, 38.0°).

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The measures (a, b, C) are about (180.5, 238.5, 145°).

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