SOLUTION: Sharon drove for part of a 150 km trop at 45 km/h and the rest of the trop at 75km/h. How far did she drive at each speed if the entire trip took her 2h 40 mins.

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Travel -> SOLUTION: Sharon drove for part of a 150 km trop at 45 km/h and the rest of the trop at 75km/h. How far did she drive at each speed if the entire trip took her 2h 40 mins.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 119977This question is from textbook
: Sharon drove for part of a 150 km trop at 45 km/h and the rest of the trop at 75km/h. How far did she drive at each speed if the entire trip took her 2h 40 mins.This question is from textbook

Answer by ankor@dixie-net.com(12701) About Me  (Show Source):
You can put this solution on YOUR website!
Sharon drove for part of a 150 km trop at 45 km/h and the rest of the trop at 75km/h. How far did she drive at each speed if the entire trip took her 2h 40 mins.
:
Let d = distance driven at 45 km/h
Then
(150-d) = distance driven at 75 km/h
:
Change 2:40 to hrs: 120 + 40 = 160 min = 160/60 = 8%2F3 hrs
:
Write a time equation: Time = distance/speed
:
Time at 45 km/hr + time at 75km/hr = 8%2F3 hrs
d%2F45 + %28%28150-d%29%29%2F75 = 8%2F3
:
Multiply equation by 450 to get rid of those annoying denominators:
:
450*d%2F45 + 450*%28%28150-d%29%29%2F75 = 450*8%2F3
:
Cancel out the denominators and we have:
10d + 6(150 - d) = 150(8)
:
10d + 900 - 6d = 1200
:
10d - 6d = 1200 - 900
:
4d = 300
:
d = 300%2F4
:
d = 75 km at 45 km/hr
then
150 - 75 = 75 km at 75 km/hr
:
:
Check solution by finding the time:
75/45 + 75/75 =
5%2F3 + 3%2F3 = 8%2F3; confirms our solutions