distance = rate

Question

It takes Amber 55 min to drive to work in the morning. She drives home using the same route, but it takes 21 min longer, and she averages 16 mi/h less than in the morning. How far does Amber drive to work?

 

What I have so far that does not come out with the correct answer:

 

d=r(11/12)

d=(r-16)(76/60)

r(11/12)=(r-16)(76/60)

-7/20r=1216/60

r=(1216/60)(-7/20)

r=-532/75

 

d=532/75(11/12)

d=1463/225

d=6.50  Which I know is not correct....What am I doing wrong?

Answer 1

You skipped a negative on the distributive step:

R(11/12)= (76/60)r -16*76/60

 

- 7/20 r = - 16*76/60

 

Then you forgot to flip the fraction over when dividing it. 

Remember KFC: KEEP FLIP CHANGE 

r= -16*76/60* -20/7

 = (16*76*20)/(60*7)

= 57 and 19/21

 

So the distance is

11/12* 1216/21= 13376/252

= 6688/126

 

76/60*(41 + 19/21)=

76/60*880/21= 66880/1260

= 6688/126 

Or just over 53 miles