Two cars leave the same town and travel in opposite directions. At the end of 8 hours, the cars are 896 miles apart. Find the rate of each car if the rate of one car is 4 mi/hr more than the rate of the other.
r and (r + 4) ---> total of 2r+4
(2r+4)8 = 896
54
To solve this problem, let's assign variables to the rates of the two cars. Let's say the rate of one car is x mi/hr. Since the rate of the other car is 4 mi/hr more, we can say the rate of the second car is x + 4 mi/hr.
Now, let's use the formula:
Distance = Rate × Time
We know that the total distance covered by both cars is 896 miles. So we have:
Distance covered by the first car + Distance covered by the second car = Total distance
Using the formula, we can write this equation:
(x mi/hr) × 8 hours + (x + 4 mi/hr) × 8 hours = 896 miles
Now, we can solve this equation to find the rate of each car:
8x + 8(x + 4) = 896
8x + 8x + 32 = 896
16x + 32 = 896
Subtracting 32 from both sides:
16x = 896 - 32
16x = 864
Dividing both sides by 16:
x = 864/16
x = 54
So, the rate of the first car is 54 mi/hr.
Now, to find the rate of the second car, we can substitute this value of x back into our equation:
Rate of the second car = x + 4
Rate of the second car = 54 + 4
Rate of the second car = 58 mi/hr
Therefore, the rate of each car is 54 mi/hr and 58 mi/hr respectively.