Greg drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Greg drove home, there was no traffic and the trip only took 5 hours. If his average rate was 21 miles per hour faster on the trip home, how far away does Greg live from the mountains?

Greg lives 280 miles from the mountains.

Step-by-step explanation:

Given:

Time required to drive to the mountains = 8 hours.

Time required to drive home = 5 hours.

We need to find the distance Greg live from the mountains.

Solution:

Let the average rate while driving to the mountains be 'x'.

So rate while returning home =

Now we know that;

Distance is equal to Speed times Time.

So we can say that;

Distance while travelling the mountain =

Distance while returning home =

Now we know that;

Distance while travelling the mountain and Distance while returning home will both be equal.

so we get;

Combining like terms we get;

Dividing both side by 3 we get;

Substituting the value of x in any of the Distance equation we get;

Distance =

Hence Greg lives 280 miles from the mountains.

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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