Question

Charmaine drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Charmaine drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Charmaine live from the mountains?

Answer 1

Charmaine lives 288 miles away from the mountains.

Step-by-step explanation:

To solve this problem, we can use the formula:

Distance = Rate x Time

Let's assume the distance Charmaine lives from the mountains is d miles.

On the way there, the trip took 9 hours and her average rate was r mph. This can be expressed as:

d = 9r

On the way back, the trip took 4 hours and her average rate was 40 mph faster than the rate on the way there, r+40. This can be expressed as:

d = 4(r + 40)

Now, we can solve the system of equations to find the distance Charmaine lives from the mountains:

9r = 4(r + 40)

Simplifying the equation, we get:

9r = 4r + 160

Subtracting 4r from both sides, we get:

5r = 160

Dividing both sides of the equation by 5, we get:

r = 32

Now, we can substitute the value of r into either equation to find the distance, d:

d = 9r

d = 9(32)

d = 288

Therefore, Charmaine lives 288 miles away from the mountains.

Answer 2

To mountains took 9 Hrs at x mph where x = No of miles to mountains
No of miles travelled = 9x

From mountains took 4 hours at (x+40) mph
No of miles travelled = 4(x+40)

Therefore 9x=4(x+40) thus 9x=4x+160 thus x=32 = distance Charmaine lives from the mountains