Two truck drivers leave a cafe at the same time, traveling in opposite direction. One truck goes 1 mph faster than the other one. After 4 hours, they are 396 miles apart. How fast is each truck going?
speed of slower = x mph
speed of faster = x+1 mph
4x + 4(x+1) = 396
8x = 392
x = 49
etc
Let's assume the speed of one truck is x mph. Since the other truck is going 1 mph faster, its speed would be (x+1) mph.
We can calculate the total distance covered by both trucks by multiplying their respective speeds with the time traveled. After 4 hours, the total distance covered would be:
Distance = Speed * Time
For the first truck: Distance1 = x * 4
For the second truck: Distance2 = (x+1) * 4
According to the problem, they are 396 miles apart. Therefore, we have the equation:
Distance1 + Distance2 = 396
Substituting the expressions for Distance1 and Distance2:
4x + 4(x+1) = 396
Now, let's solve this equation step-by-step:
4x + 4x + 4 = 396
Combine like terms:
8x + 4 = 396
Subtract 4 from both sides:
8x = 392
Divide both sides by 8:
x = 49
Therefore, one truck is traveling at 49 mph, and the other truck, which is going 1 mph faster, is traveling at (49+1) = 50 mph.
To solve this problem, we can set up a system of equations based on the given information. Let's denote the speed of the slower truck as "x" mph. Since the other truck is going 1 mph faster, its speed will be "x + 1" mph.
We know that the distance traveled by each truck is equal to its speed multiplied by the time traveled. In 4 hours, the slower truck will have traveled a distance of 4x miles, and the faster truck will have traveled a distance of 4(x + 1) miles.
Since they are traveling in opposite directions, the sum of their distances should equal the total distance apart, which is 396 miles. So, we can set up the equation: 4x + 4(x + 1) = 396.
Now, let's solve this equation step by step:
4x + 4x + 4 = 396
8x + 4 = 396
8x = 396 - 4
8x = 392
x = 392 / 8
x = 49
Therefore, the slower truck is going at a speed of 49 mph, and the faster truck is going at a speed of (49 + 1) mph, which is 50 mph.
So, the speed of each truck is 49 mph and 50 mph, respectively.