SOLUTION: Gerry and Tony live 11km apart. Gerry leaves his home at 2 p.m. and bikes toward Tony's home at 25 km/hr. At the same time, Tony leaves his home and bikes toward Gerry's home at 30

Question 175901This question is from textbook algebra 1
: Gerry and Tony live 11km apart. Gerry leaves his home at 2 p.m. and bikes toward Tony's home at 25 km/hr. At the same time, Tony leaves his home and bikes toward Gerry's home at 30 km/hr as soon as they reach each other's homes they turn around and start back along the same route. They stop when they meet each other on the ride back to their own homes. How far are they are from Gerry's home when they stop?This question is from textbook algebra 1

Answer by josmiceli(6784) (Show Source):
You can put this solution on YOUR website!
For both,

Each has their own rates, times and distances, so
Tony's equation
Gerry's equation
Each bikes to the others house and they leave at the same time, so
For Tony,

hrs
and, for Gerry,

hr
Comparing these, with LCD

So, Tony got to Gerry's house hrs quicker
than Gerry got to Tony's house.
-------------------
Now, they turn around and head back toward eachother.
If they left at the exact same time, the elapsed
time for each until they met would be the same
, but Tony gets a head start.
-------------------
Assume I have a stopwatch and I'm in a helicopter overhead
so I can see both of them. I'll start the stopwatch when
Gerry turns around hr after Tony has turned around.
If Gerry's time to where they meet from Tony's house is
then Tony's time from Gerry's house is
--------------------
Now my equations are
km

where these are the distances each travel to where they meet
(1)
(2)
rewriting (1)
(1)
Substitute (2) in (1)

hr
hrs or min
------------------
The distance Tony travels is the distance from Gerry's
house when they meet
(1)

km
They meet 7 km from Gerry's house
check answer:
(2)

and
km

OK