SOLUTION: Jerry drives 500km to a teachers convention. On the return trip, he increases his speed by 25 km/hr and saves 1 hr of driving time. How fast did he go in each direction?

Algebra ->  Equations -> SOLUTION: Jerry drives 500km to a teachers convention. On the return trip, he increases his speed by 25 km/hr and saves 1 hr of driving time. How fast did he go in each direction?       Log On


   

Question 1042107: Jerry drives 500km to a teachers convention. On the return trip, he increases his speed by 25 km/hr and saves 1 hr of driving time. How fast did he go in each direction?


Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Travel rate rule for rate R, time T, distance D, is RT=D. 

VARIABLES
r     unknown rate going
t     unknown time, going
d     distance either way.  d=500.
k     amount of added speed going back.  k=25.
h     amount of less time going back.  h=1.


                  RATE       TIME       DISTANCE
TO                 r         t           d
FROM              r+k        t-h         d

Form the necessary system of equations and solve for r and t.

The NECESSARY equations each come from the fundamental travel rates rule and the two one-way trips.
system%28rt=d%2C%28r%2Bk%29%28t-h%29=d%29, in keeping all in variables, both unknown and known variables. The idea here is to solve the system purely in variables AND THEN substitute the known values. The two UNKNOWN VARIABLES are r and t.

Here are a couple of possible first steps.
%28r%2Bk%29%28t-h%29=d
rt%2Bkt-rh-hk=d
And a substitution for d using the "GOING TO" equation,
rt%2Bkt-rh-hk=rt
rt%2Bkt-rh-hk-rt=rt-rt
kt-rh-hk=0
but now, YOU CONTINUE THIS.....