Two motorcyclists start at the same point and travel in opposite directions. One travel 3 mph faster than the other. In two hours they are 206 miles apart. How fast is each traveling?
The speed of the slower motorcyclist is ___ mph.
speed of slower ---- x mph
speed of faster ---- x+3 mph
after 2 hours:
distance covered by slower = 2x
distance covered by faster = 2(x+3)
solve
2x + 2(x+3) = 206
.
.
so is the answer 50
You tell me .
Does that answer work for the original conditions?
i think so but the answer suppose to be in the form of x and y
Are you looking at the answers to this question?
There is no need for two variables
I defined x to be the slower speed, and x = 50
I defined x+3 to be the faster speed, or x+3 = 53
distance covered by slower in 2 hours = 2(50) = 100 miles
distance covered by faster in 2 hours = 2(53) = 106
and what is 100+106 ? ...
looks good to me.
206
so what is the speed of the slower biker ?
53
good!
To find the speed of each motorcyclist, we can set up a system of equations.
Let's assume the speed of the slower motorcyclist is x mph.
Since the other motorcyclist is traveling 3 mph faster, their speed would be (x + 3) mph.
In 2 hours, the slower motorcyclist would have traveled a distance of 2x miles, and the faster motorcyclist would have traveled a distance of 2(x + 3) miles.
Since they are traveling in opposite directions, their distances would add up to 206 miles, so we can set up the equation:
2x + 2(x + 3) = 206.
Simplifying the equation:
2x + 2x + 6 = 206,
4x + 6 = 206,
4x = 206 - 6,
4x = 200.
Dividing both sides of the equation by 4:
x = 50.
Therefore, the speed of the slower motorcyclist is 50 mph.