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.