On Wednesday Roman drove to work in 45 minutes On Thursday h

On Wednesday, Roman drove to work in 45 minutes. On Thursday he averaged 12miles per hour more, and it took him 9 minutes less to get to work. Hoew far does he travel to work?

Solution

distance(d)=rate(r) times time(t) or d=rt;r=d/t and t=d/r
Let d=distance to work
And let r=his rate on Wednesday
Then r+12=his rate on Thursday
distance to work on Wed=rt=r*45 or 45r
distance to work on Thursday=rt=(r+12)*(45-9)=36(r+12)
distance to work on Wed=distance to work on Thu. So our eq to solve is:
45r=36(r+12) get rid of parens
45r=36r+432 subtract 36 from both sides
45r-36r=432 collect like terms
9r=432 divide both sides by 9
r=48mph--------------------rate on Wed
r+12=48+12=60mph---------------rate on Thu
d=rt=48*(3/4)=36 mi (Wed)(note:45 min=3/4 hr)--------------------Ans
d=rt=60*(3/5)=36 mi (thu)(note: 36 min=3/5hr)