SOLUTION: Jose and Eduardo are going to run a race. Jose is willing to give Eduardo a 3 mile head start. Jose runs at a rate of 7.5 miles per hour. Eduardo's rate is 1.5 miles per hour SLOWE

Algebra ->  Systems-of-equations -> SOLUTION: Jose and Eduardo are going to run a race. Jose is willing to give Eduardo a 3 mile head start. Jose runs at a rate of 7.5 miles per hour. Eduardo's rate is 1.5 miles per hour SLOWE      Log On


   

Question 1073991: Jose and Eduardo are going to run a race. Jose is willing to give Eduardo a 3 mile head start. Jose runs at a rate of 7.5 miles per hour. Eduardo's rate is 1.5 miles per hour SLOWER that Jose.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Eduardo's rate is 6 miles per hour. If he had the 3 mile head start, then for this distance he had run 3%2F6=1%2F2, half an hour. 


d is the distance they both go when Jose catches up with Eduardo.
t is how long it takes for Jose to reach Eduardo.

              SPEED     TIME      DISTANCE
JOSE           7.5        t        d
EDUARDO        6         t+1/2     d


If solve for time only, t for how long to catchup,
highlight_green%287.5t=6%28t%2B1%2F2%29%29


-
7.5t=6t%2B3
1.5t=3
t=3%2F1.5
highlight%28t=2%29-----catching-up time 2 hours


RACING DISTANCE d:
-
7.5%2A2=15
or
6%282%2B1%2F2%29
12%2B3
15
-
highlight%28d=15%29--------- 15 mile race

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Jose and Eduardo are going to run a race. Jose is willing to give Eduardo a 3 mile head start.
Jose runs at a rate of 7.5 miles per hour. Eduardo's rate is 1.5 miles per hour SLOWER that Jose.
~~~~~~~~~~~~~~~~~~~~~~~~~ 

Your equation is this:

7.5*t = 3 + 6*t

The solution is

7.5t - 6t = 3,

1.5t = 3  --->  t = 3%2F1.5 = 2 hours.

Answer.  Jose catches up Eduardo in 2 hours.


Writing by "josgarithmetic" (including his equation) is WRONG, NONSENSICAL and does not correspond to the condition..


It would be good (much better) if you put a question in your post.