Jack travels to work on the eastern freeway. he notices that the difference in time between if he drives 5 mph below the speed limit an if he drives 15 mph below the speed limit is 2 minutes. given that the distance for which he uses the freeway is 10 miles.. find the speed limit of the freeway

Remark

Interesting question. He goes 10 miles no matter what his speed. Let the speed limit = x

Givens

d = 10 miles

r - 5 mph = r1

r - 15 mph = r2

t = 2 minutes

t = 2/60 = 1/30 hours

Formula

10/(r - 15) - 10/(r - 5) = 1/30 hours Take out the common factor of 10

Sub and solve

10 (1 / (r - 5) - 1/(r - 15) ) = 1/30 Divide by 10

1/(r - 15) - 1/(r - 5) = 1/300

Put over a common denominator. (r - 5)(r - 15)

Cross multiply

300 * 10 = (r - 5)(r - 15) Remove the brackets.

3000 = r^2 - 20r + 75 Add 3000 to both sides.

r^2 - 20r - 2925 = 0

The monster factors (believe it or not)

(r - 65)(r + 45) = 0

The rate that works is

r - 65 =0

r = 65

The other rate is - 45 and it has no meaning.

Surely your were not expected to do this as I have done it.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6