You and a friend are running on treadmills you run 0.5 miles every 3 minutes and your friend runs 2 miles every 14 minutes. you both start and stop running at the same time and run a whole number of miles. what is the least possible number of miles you and your friend can run?

7 miles and 6 miles respectively.

Step-by-step explanation:

For me,

Distance = 0.5 miles,

Time = 3 minutes,

So, pace = = = 6 minute per miles,

That is, I am running 1 mile in 6 minutes.

For my friend,

Distance = 2 miles,

Time = 14 minutes,

So, pace = = 14 minutes per mile,

That is, my friend is running 1 mile in 7 minutes,

Thus, the time after we will meet = LCM(6,7) = 42 minutes,

Also, my speed =

miles per minute,

Similarly my friend's speed = = miles per minute,

In 42 minutes,

Distance covered by me = = 7 miles,

Distance covered by my friend = = 6 miles.

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.

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour