Two men starting at a point on a circular 1-mile race track walk in opposite directions with uniform speeds and meet in 6 minutes, but if they walk in the same direction, it requires one hr for the faster walker to gain a lap. What is the rate of the slower walker?

The rate of the slower walker is 4.5 mph.

Step-by-step explanation:

Let the speed of the faster walker is x mph and that of the slower walker is y mph.

So, when they are moving in the opposite direction starting from the same point at the same time, then their resultant speed id (x + y) mph

Now, given that, ............. (1)

Again, when they are moving in the same direction, then their resultant speed will be (x - y) mph.

And as per the given conditions,

............. (2)

Now, solving equations (1) and (2) we get,

2x = 11

⇒ x = 5.5 mph and from equation (2),

y = x - 1 = 4.5 mph.

Therefore, the rate of the slower walker is 4.5 mph. (Answer)

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simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .