Hello, tlneader!
Spike averaged 45mph driving from Rochester to Syracuse and 49 mph from Syracuse to Albany.
If he drove 237 miles in 5 hours, how far is it from Syracuse to Albany?
\(\displaystyle x\,+\,y\:=\:237\)
\(\displaystyle 45x\,+\,49y\:=\:5\;\;\) . . . This is wrong
You really should name the variables first.
Let \(\displaystyle x\) = distance from Rochester to Syracuse.
Let \(\displaystyle y\) = distance from Syracuse to Albany.
Your first equation is correct.
The total distance is 237 miles: \(\displaystyle \L\,x\,+\,y\:=\:237\;\)
[1]
You second equation makes no sense.
\(\displaystyle 45x\) = 45 mph times \(\displaystyle x\) miles
\(\displaystyle \;\;\)What is that? \(\displaystyle \;\)It is
not the number of hours.
We have: \(\displaystyle \,\text{Distance } = \text{ Speed }\times\text{ Time}\;\;\Rightarrow\;\;\text{Time }=\;\frac{\text{Distance}}{\text{Speed}}\)
He drove \(\displaystyle x\) miles from Rochester to Syracuse at 45 mph: Time = \(\displaystyle \frac{x}{45}\) hours.
He drove \(\displaystyle y\) miles from Syracuse to Albany at 49 mph: Time = \(\displaystyle \frac{y}{49}\) hours.
Total driving time is 5 hours: \(\displaystyle \L\:\frac{x}{45}\,+\,\frac{y}{49}\:=\:5\;\)
[2]
Now solve
that system of equations . . .
:lol: