Math Is Fun Forum

tabby

Member

Registered: 2009-12-07

Posts: 2

Plz help with this FORMULA

My replacement test is approaching and I am having troubles with some excercices :
Here is an example:

The formula D = 0.054x2 + 0.058x describes the distance in feet D that it takes to stop a
vehicle traveling x miles per hour on dry pavement.
a. How fast can you drive if you wish to be able to stop your car within 65 feet?
b. On black ice, a truck’s stopping distance is 3 times its stopping distance on dry pavement. A
truck traveling 20 miles per hour applies the brakes, on black ice, at a distance of 65 feet in front
of a rubber traffic cone. Will the truck hit the cone?
_________________________________________________________________________________
In the planning stages of the renovation of an 1800-square-foot space, the amount of office
space allocated per person is increased by 25 square feet when 6 people are removed to a n
adjoining building. How many people share this renovated space after the move?
How much space does each person have?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Plz help with this FORMULA

For the first part, D=65, so the equation is 65 = 0.054x² + 0.058x.
Solve this quadratic equation, and you'll find the maximum speed you can be travelling.
(There will be two solutions, but one of them will be negative, so you can ignore it)

The second is easier, because you just need to put the numbers in and see what happens.
The formula for braking distance is now D = 3(0.054x² + 0.058), so put in the value of x that you're given and see if it'll stop before it hits the cone or not.

For the third question, write equations displaying the information about before and after the renovation.

ie. If the original amount of workers was w, and they originally had s m² of space, then:
ws = 1800

After the renovation, 6 workers got moved but each remaining worker got 25m² more space, so:
(w-6)(s+25) = 1800

Now you have two simultaneous equations in two variables, which you can solve to find w and s.

---

Why did the vector cross the road?
It wanted to be normal.