Bill and Joe leave their house at the same time heading in opposite directions. If Bill is driving three times faster than Joe and it takes them three hours to be 120 miles apart, how fast is Bill driving?
Bill is driving at 30mph
Joe drives X mi/h.
Bill drives 3x mi/h.
3x + 3(3x) = 120.
X = ?.
3X = ?.
To find Bill's speed, we need to first determine Joe's speed.
Let's assume Joe's speed is x mph.
Since Bill is driving three times faster than Joe, Bill's speed is 3x mph.
We are given that it takes them three hours to be 120 miles apart.
To find Joe's speed, we use the formula:
Distance = Speed × Time
For Joe:
Distance = x mph × 3 hours
For Bill:
Distance = 3x mph × 3 hours
Since they are traveling in opposite directions, the sum of their distances will be equal to the total distance between them:
Distance for Joe + Distance for Bill = Total Distance
x mph × 3 hours + 3x mph × 3 hours = 120 miles
Now, we can simplify the equation and solve for x:
3x + 9x = 120
12x = 120
x = 120 / 12
x = 10
Therefore, Joe's speed is 10 mph.
To find Bill's speed:
Bill's speed = 3 × Joe's speed
Bill's speed = 3 × 10 mph
Bill's speed = 30 mph
So, Bill is driving at 30 mph.
3x(3) + 3(x) = 120
9x + 3x =120
12x = 120
x=10