A Double Sound of Hammering.

Let's go easy. This is simple speed problem. Lets take the distance as x , and the time taken as t i.e. the time taken through the rail. Now, as per the question goes the time taken through the air is " $t+6$ " .

So acc. to the question : $\frac {x}{16500}=t$ ......................... (1)

Also : $\frac {x}{1100}=t+6$ .................................................................................... (2)

Solvig these two equation we get $t=0.428571$ ........... then we get $x=7071.4$ .

So got it. Quite easy atleast gave me 100 points. :)

Enjoy

Everybody's Friend

Arya.

$Speed:\quad { V }_{ 1 }{ >V }_{ 2 }\\ Time\quad T_{ 1 }<{ T }_{ 2 }\\ Displacement:\quad X={ V }_{ 1 }T_{ 1 }{ =V }_{ 2 }T_{ 2 }\\ \\ T_{ 2 }-T_{ 1 }=6\\ { V }_{ 1 }T_{ 1 }=6{ V }_{ 2 }+{ V }_{ 2\\ }T_{ 1 }\\ T_{ 1 }({ V }_{ 1 }{ -V }_{ 2 })=6{ V }_{ 2 }\\ T_{ 1 }=\frac { 6{ V }_{ 2 } }{ { V }_{ 1 }{ -V }_{ 2 } } =0.428571429\\ \\ X={ V }_{ 1 }{ T }_{ 1 }=7071.428571429$

lets required distance is "x" time taken by sound through steel=x/16500 time taken by sound through air=x/1100 since diff bw time is 6 sec x/1100-x/16500=6 x=7071.428571

Let's suppose that the distance of me and the spike is 1100\times t, and t is the time that the sound travels through the air. So, if the sound arrives 6 seconds before through the rail, we have 1100t = 16500(t-6) 16500\times 6 = t(16500-1100) t = 165 \times 6/154 t = 90/14 = 45/7

If we are far away from the spike about 1100t, we have: D = 1100\times 45/7 = 49500/7 = 7071,4 approximately

easy, let the time taken by the sound to travel by rail be t sec. so the time by air is (t+6) sec now let the path travelled be x. we know, s=vt so, 16500t=1100(t+6) from here, t=0.43 now put it in the equation s=vt and u get the answer.

thanks, this is my first solvedproblem in brilliant... cheers!!!!!!!!

16,500 (t-6) = 1,100t

16,500t - 99,000 = 1,100t

15,400t = 99,000

t = $\frac{99,000}{15,400}$ = $\frac{45}{7}$

s = $v \times t$ = $1,100 \times \frac{45}{7}$ = 7071.4 approximately

that was so ec , just use the substitution method ...1100 ft/s=d/x+6 , x is ur time and the other one would be 16500 ft/s=d/x using sub method ur d will be 16500x, substituting it to the other equation it will cr8 an eq. of 1100ft/s=16500x/x+6 then we would have 1100x-16500x=-6600 using the transposition method after dividing it our x will be 0.42857 and "NOW" u can freely choose to what eq. u want to work with and what u have to do is to sub. that into ur x and u will have the answer of "7071.4!!"