two motorcyclists started at the same point and travel in opposite directions. one travels 6 mph faster than the other.In 4 hours they are 432miles apart. how fast is each traveling?
speed of slower mph
speed of faster mph
let speed of slower be x mph
then speed of the faster is x+6 mph
distance covered by slower = 4x
distance covered by faster = 4(x+6)
4x + 4(x+6) = 432
8x + 24=432
8x = 408
x = 51
the slower went 51 mph, the faster went 57 mph
Let's call the speed of the slower motorcyclist "x" mph. Since the other motorcyclist is traveling 6 mph faster, we can represent their speed as "x + 6" mph.
In 4 hours, the combined distance covered by both motorcyclists is 432 miles. This means that the slower motorcyclist travels a distance of 4x miles, and the faster motorcyclist travels a distance of 4(x + 6) miles.
Given that the total distance covered is 432 miles, we can set up the following equation:
4x + 4(x + 6) = 432
To solve for x, we simplify the equation:
4x + 4x + 24 = 432
8x + 24 = 432
Subtracting 24 from both sides:
8x = 408
Dividing both sides by 8:
x = 51
Therefore, the speed of the slower motorcyclist is 51 mph, and the faster motorcyclist is traveling at a speed of 51 + 6 = 57 mph.
To find the speeds of the two motorcyclists, let's assign variables to the unknown quantities.
Let's say the speed of the slower motorcyclist is "x" mph.
Since the faster motorcyclist is traveling 6 mph faster than the slower one, their speed can be represented as "x + 6" mph.
Now, let's set up equations based on the given information:
Distance = Speed * Time
For the slower motorcyclist:
Distance = x mph * 4 hours
For the faster motorcyclist:
Distance = (x + 6) mph * 4 hours
According to the problem, the total distance covered by both motorcyclists is 432 miles:
(x mph * 4 hours) + ((x + 6) mph * 4 hours) = 432 miles
Simplifying the equation:
4x + 4(x + 6) = 432
Now, solve the equation:
4x + 4x + 24 = 432
8x + 24 = 432
8x = 432 - 24
8x = 408
x = 408 / 8
x = 51
Therefore, the speed of the slower motorcyclist is 51 mph.
To find the speed of the faster motorcyclist:
x + 6 = 51 + 6 = 57
Therefore, the speed of the faster motorcyclist is 57 mph.