Rueben drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
7
hours. When Rueben drove home, there was no traffic and the trip only took
5
hours. If his average rate was
18
miles per hour faster on the trip home, how far away does Rueben live from the mountains?
315
To find out how far Rueben lives from the mountains, we can use the formula:
Distance = Rate × Time
Let's assume that the distance from Rueben's home to the mountains is D miles.
On the way to the mountains, Rueben took 7 hours and his average rate was R mph. Therefore, the equation would be:
D = R × 7
On the way back from the mountains, Rueben took 5 hours and his average rate was (R + 18) mph. Therefore, the equation would be:
D = (R + 18) × 5
Now we have a system of two equations:
D = 7R (Equation 1)
D = 5(R + 18) (Equation 2)
To solve this system, we can substitute Equation 1 into Equation 2:
7R = 5(R + 18)
Simplifying the equation:
7R = 5R + 90
Subtracting 5R from both sides:
2R = 90
Dividing by 2:
R = 45
Now we can substitute this value back into Equation 1 to find the distance D:
D = 7 × 45
D = 315
Therefore, Rueben lives approximately 315 miles away from the mountains.