solving with substitution new new new

[tlneader]

New word problem:

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?

x+y=237

45x+49y=5

I am having trouble solving for x. Do the equasions look correct

 

[galactus]

Your equations are correct. You must've entered it in wrong. My calculator gave me the right answer with the equations you have.

 

[Denis]

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?
x+y=237
45x+49y=5
I am having trouble solving for x. Do the equasions look correct

x = distance Syracuse to Albany; then distance Rochester to Syracuse = 237 - x

time S to A = x / 49
time R to S = (237 - x) / 45

Since total time = 5, then:
x / 49 + (237 - x) / 45 = 5
Solve for x

 

[soroban]

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 . . .

 

[galactus]

Please start a new thread when you have another problem. Since you changed your problem, the calculations from the previous problem are no longer relevant.

 

[Denis]

Hey galactus: your solution is entirely WRONG :roll:

 

[galactus]

No, Denis, it is not. There was an entirely different problem posted initially. The poster deleted it and posted another instead of starting a new thread. I think I will delete the post. It looks ridiculous now.

 

[Denis]

No, Denis, it is not. There was an entirely different problem posted initially. The poster deleted it and posted another instead of starting a new thread. I think I will delete the post. It looks ridiculous now.

Hey, I was JOKING!! :wink:

 

[galactus]

You got me. After I replied, I thought maybe you were. :lol: