Answer:
27mph
Explanation:
Let's assume the speed of the first car is x mph. Since the second car is traveling 6 mph slower, its speed would be (x - 6) mph.
To find out how far each car has traveled, we can use the formula: distance = speed × time.
For the first car:
Distance traveled by the first car = speed of the first car × time
d₁ = x mph × (4 hours + 20 minutes)
Since we need to work with a single unit of time, let's convert 20 minutes to hours:
20 minutes = 20/60 = 1/3 hours
Substituting the values:
d₁ = x mph × (4 + 1/3) hours
d₁ = x mph × (13/3) hours
d₁ = (13x/3) miles
For the second car:
Distance traveled by the second car = speed of the second car × time
d₂ = (x - 6) mph × (4 hours + 20 minutes)
d₂ = (x - 6) mph × (13/3) hours
d₂ = (13/3)(x - 6) miles
Since they are traveling in opposite directions, the sum of their distances is equal to the total distance between them:
d₁ + d₂ = 260 miles
Substituting the expressions for d₁ and d₂:
(13x/3) + (13/3)(x - 6) = 260
To simplify the equation, let's multiply both sides by 3 to get rid of the denominators:
13x + 13(x - 6) = 780
13x + 13x - 78 = 780
26x - 78 = 780
26x = 780 + 78
26x = 858
x = 858/26
x ≈ 33
The speed of the first car is approximately 33 mph. Substituting this value back into the equation for the speed of the second car:
Speed of the second car = x - 6 ≈ 33 - 6 ≈ 27 mph
Therefore, the first car is traveling at approximately 33 mph, and the second car is traveling at approximately 27 mph.