Two new word problems I can't seem to solve.

[mkay]

This first one I thought I had solved, but when we did it in class, I had it wrong. The problem is when I tried to continue it at home, I keep getting different answers for the distance and the distance is supposed to be the same.

A spike is hammered into a train rail. You are standing at the other end of the rail. You hear the sound of the hammer strike both through the air and through the rail itself. These sounds arrive at your point six seconds apart. You know that sound travels through air at 1100 ft. per second and through steel at 16500 ft. per second. How far away is that spike? (round to one decimal place.)

d = 1100(t + 6 ), d = 16500t, so 1100(t + 6) = 16500t
1100t + 6600 = 16500t, 1100t - 1100t + 6600 = 16500t-1100t, 6600 = 15400t
6600/15400 = 15400t/15400, 0.4285 = t, 1100(.4285 + 6) = 7071.35, 16500(.4285) = 7070.25. Why are they different?

Also, Frank is eight years older than his sister. In three years he will be twice as old as she is. How old are they now? I can't even figure out how to set this up. thanks for your help.

 

[cordoba]

For the first one, it's because you're rounding the value of t = 6600/15400 to 0.4285. If you plug in 6600/15400 for t in both equations, you will get the same answer ~ 7071.43 (approximately)

 

[cordoba]

For the second, let F be Frank's age and S be his sister's age.

Then, the first statement, "Frank is eight years older than his sister." would be F = 8 + S (Frank's age is 8 years more than his sister's).

"In three years he will be twice as old as she is"

Here we are comparing their ages in 3 years, so we are comparing F + 3 and S +3 (their ages plus 3 years)
We know in 3 years Frank will be twice as old as his sister, so

F + 3 = 2(S + 3)

Frank's age in 3 years will be 2 times his sister's age in 3 years.

You can solve these 2 for F and S.

 

[soroban]

Hello, mkay!

A spike is hammered into a train rail. You are standing at the other end of the rail.
You hear the sound of the hammer strike both through the air and through the rail itself.
hese sounds arrive at your point six seconds apart.
ou know that sound travels through air at 1100 ft. per second and through steel at 16500 ft. per second.
How far away is that spike? (round to one decimal place.)

Use the formula: .\(\displaystyle \text{Time} \:=\:\dfrac{\text{Distance}}{\text{Speed}} \)

Let \(\displaystyle x\) = distance to the spike.

The sound travels \(\displaystyle x\) feet at 1100 ft/sec through the air.
. . This takes: /\(\displaystyle \frac{x}{1100}\) seconds.

The sound travels \(\displaystyle x\) feet at 16,500 ft/sec through steel.
. . This takes: .\(\displaystyle \frac{x}{16,500}\) seconds.

The time through the air is 6 seconds more than the time through steel.

. . \(\displaystyle \dfrac{x}{1100} \;=\;\dfrac{x}{16,500} + 6 \)


Can you finish it now?

 

[mkay]

Thanks for yoyr help

Thanks appreciate your help, both of you.

 

[zoobeast]

still don't get it. How about showing all the steps you used to solve this.

u

For the second, let F be Frank's age and S be his sister's age.

Then, the first statement, "Frank is eight years older than his sister." would be F = 8 + S (Frank's age is 8 years more than his sister's).

"In three years he will be twice as old as she is"

Here we are comparing their ages in 3 years, so we are comparing F + 3 and S +3 (their ages plus 3 years)
We know in 3 years Frank will be twice as old as his sister, so

F + 3 = 2(S + 3)

Frank's age in 3 years will be 2 times his sister's age in 3 years.

You can solve these 2 for F and S.