SOLUTION: On Monday, Carlos drove to work in 35 minutes. On Tuesday, he averaged 9 miles per hour more and arrived 7 minutes faster. How far (in miles) does Carlos travel from home to wo

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: On Monday, Carlos drove to work in 35 minutes. On Tuesday, he averaged 9 miles per hour more and arrived 7 minutes faster. How far (in miles) does Carlos travel from home to wo      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 389296: On Monday, Carlos drove to work in 35 minutes. On Tuesday, he averaged 9 miles per hour more and arrived 7 minutes faster. How far (in miles) does Carlos travel from home to work?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
On Monday, Carlos drove to work in 35 minutes.
On Tuesday, he averaged 9 miles per hour more and arrived 7 minutes faster.
How far (in miles) does Carlos travel from home to work?
:
Let d = distance traveled to work
Let s = average speed on monday
then
(s+9) = average speed on tuesday
:
Write two time equations: time = dist/speed
d%2Fs = 35%2F60
Cross multiply
60d = 35s
Simplify, divide by 5
12d = 7s
12d - 7s = 0
and
d%2F%28%28s%2B9%29%29 = 28%2F60; (7min faster)
Cross multiply
60d = 28(s+9)
60d = 28s + 252
Simplify, divide by 4
15d = 7s + 63
15d - 7s = 63
:
Subtract the 12d - 7s = 0 from the above equation
15d - 7s = 63
12d - 7s = 0
----------------subtraction eliminates s, find d
3d = 63
d = 63%2F3
d = 21 miles is C's distance to work
:
:
Check this: find the the speed
7s = 12(21)
7s = 252
s = 252/7
s = 36 mph
:
Find the times
21/36 = .583 hrs
21/45 = .467 hrs; (9 mph faster)
-----------------
difer = .116 hrs which is about 7 min