Marcus can walk 1 mile to the library in the same time he can bicycle 2.5 miles to the sporting goods store. His speed on the bicycle is 6 mi/h faster than his walking speed. What is his speed walking?
Let's assume Marcus's walking speed is x mi/h.
His speed on the bicycle is x + 6 mi/h.
The time it takes for him to walk 1 mile is given by 1/x.
The time it takes for him to bicycle 2.5 miles is given by 2.5/(x + 6).
According to the problem, these times are equal, so we can set up the following equation:
1/x = 2.5/(x + 6)
To solve this equation, we can cross-multiply:
x(x + 6) = 2.5(1)
x^2 + 6x = 2.5
x^2 + 6x - 2.5 = 0
To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 6, and c = -2.5
x = (-6 ± √(6^2 - 4(1)(-2.5))) / (2(1))
x = (-6 ± √(36 + 10)) / 2
x = (-6 ± √46) / 2
Simplifying further, we have:
x = (-3 ± √46) / 2
Since we're interested in Marcus's walking speed, which is positive, we take the positive value:
x = (-3 + √46) / 2
Therefore, Marcus's walking speed is approximately 1.79 mi/h.