nas went on a road trip

Question

nas went on a 220 mile trip to a soccer game. on the way back she had to drive 11 miles per hour slower. this made the trip an hour longer. how fast did she did she drive to the soccer game

Answer 1

Distance = rate*time ...  d=rt

 

Let r = speed to the game

Let t = time to soccer game

 

rate from soccer game = (r-11)

Time from soccer game = (t+1)

 

To soccer game:

equation 1:   220 = rt

 

From soccer game:

equation 2:  220 = (r-11)(t+1)

 

We have 2 equations:

1.  rt = 220

2.  (r-11)(t+1) = 220

 

We want to find r ... in equation 1 solve for t in terms of r

and substitute into equation 2

t = 220/r

 

(r-11)(220/r + 1) = 220

r(220/r) + r(1) + (-11)(220/r) + (-11)(1) = 220

220 + r - 2420/r - 11 = 220

r - 2420/r + 209 = 220

r - 2420/r - 11 = 0

Multiply everything by r

 

r² - 2420 - 11r = 0

 

We have a quadratic:

r^r - 11r - 2420 = 0

 

We can factor this:

The factors of -2420 that add to -11 are (-55)(44)

(r-55)(r+44) = 0

 

Either r-55=0   or   r+44=0

         r=55      or    r=-44

 

Since the speed will not be negative, discard r=-44

 

The rate going to the soccer game was 55 mph