SOLUTION: I am in an online college class for algebra 2 and get stuck on word problems quite easily. This is the problem: Elena bicycles 6 km/h faster than Javier. In the same time it takes

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Question 555998: I am in an online college class for algebra 2 and get stuck on word problems quite easily. This is the problem: Elena bicycles 6 km/h faster than Javier. In the same time it takes Javier to bicycle 57 km, Elena can bicycle 75 km. How fast is both bicyclist traveling?
Found 3 solutions by ankor@dixie-net.com, stanbon, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Elena bicycles 6 km/h faster than Javier.
In the same time it takes Javier to bicycle 57 km, Elena can bicycle 75 km.
How fast is both bicyclist traveling?
:
Let s = J's speed
then
(s+6) = E's speed
:
Write a time equation: time = dist/speed
:
75%2F%28%28s%2B6%29%29 = 57%2Fs
Cross multiply so find s

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Elena bicycles 6 km/h faster than Javier. In the same time it takes Javier to bicycle 57 km, Elena can bicycle 75 km. How fast is both bicyclist traveling?
--------------
Javier DATA:
rate = x km/h ; distance = 57 km ; time = d/r = 57/x hrs.
-----
Elena DATA:
rate = (x+6) km/h ; distance = 75 km ; time = d/r = 75/(x+6) hrs
======================
Equation:
time = time
57/x = 75/(x+6)
75x = 57(x+6)
75x-57x = 6*57
18x = 6*57
x = (1/3)57
x = 19 km/h (Javier's rate)
x+6 = 25 km/h (Elena's rate)
================================
Cheers,
Stan H.
=================

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need 2 equations: 1 for Elena and 1 for Javier
Let +s+ = Javier's speed in km/hr
Let +t+ = the time for both
------------------------
Javier's eqution:
(1) +57+=+s%2At+
Elena's equation:
(2) +75+=+%28+s+%2B+6+%29%2At+
-----------------
This is 2 equations and 2 unknowns, so it's solvable
(1) +t+=+57%2Fs+
substitute (1) into (2)
(2) +75+=+%28+s+%2B+6+%29%2A%2857%2Fs%29+
(2) +75+=+57+%2B+342%2Fs+
(2) +75s+=+57s+%2B+342+
(2) +18s+=+342+
(2) +s+=+19+
+s+%2B+6+=+19+%2B+6+
+s+%2B+6+=+25+
Javier's speed is 19 km/hr
Elena's speed is 25 km/hr
check answer:
(1) +t+=+57%2Fs+
(1) +t+=+57%2F19+
(1) +t+=+3+ hrs
and
(2) +75+=+%28+s+%2B+6+%29%2At+
(2) +75+=+25t+
(2) +t+=+75%2F25+
(2) +t+=+3+ hrs
OK