Physics Question?

Question

How do you set up this equation? I solved, or thought I solved for t and got 15, but something's not adding up...


A man is walkng at an average speed of 4 miles per hour alongside a railroad track. A train going in the same direction at an average speed of 30 miles per hour requires 5 seconds to pass the man. How long is the train in feet?

Answer 1

L = [VtT - VmT] 5280
Vt = 30 mph
Vm = 4 mph
T = 5 sec = 5/60 hrs
5280 ft = 1 mile

L = [30(5/60) - 4(5/60)] 5280
L = 11,440 feet

Answer 2

Let's get everything in feet per second, and then take a look at the problem.

1 mile/hour x 5280 ft/mi / 3600 sec/hr = 22/15 ft/sec.
The man's speed is 88/15 ft/sec, and the train's speed is 44 ft/sec.

Now let's set up the problem. Suppose the length of the train is x. At time t = 0, the front of the train is next to the man. At time t = 5 the back of the train is next to the man. In 5 seconds, the man walked 5(88/15) = 88/3 feet. In that same 5 seconds, the back of the train moved x + 88/3 feet (the length of the train plus the distance the man walked).

Speed is distance/time, so for the back of the train (which travels as fast as the front of the train), we have

44 ft/sec = (x + 88/3) ft / 5 sec
220 = x + 88/3
x = 220 - 88/3 = (660 - 88)/3 = 572/3 = 190 feet, 8 inches
(or 190 2/3 feet, if you prefer).

That's the answer.

Another, perhaps easier, way to get it is to realize that in 5 seconds, the front of the train goes 5 x 44 = 220 feet, while the man walks 5 x 88/15 = 88/3 feet. The length of the train is 220 minus 88/3 feet. That gives you the same answer.

Answer 3

Hi,
It's 190.667 ft.

Time = 5/3600 hours
Dm = rate x times = 20/3600
Distance it takes the train to pass him is the length of the train plus the distance the man walked. So
Dt=150/3600 miles
So the length of the train is (150/3600)-(20/3600)=130/3600 mi.

convert to feet (130/3600)(5280/1)=190.6666 ft.

Answer 4

The speed of the train relative to the man is 26mph. D=vt, or in this case 24mpn*(5/3600)h=.03333mi At 5280 ft per mile, this is 176 ft

Edit: the second line should read "26mph*(5/3600)h=.036111; At 5280 ft per mile, this is 190.67 ft"

Answer 5

the answer is .....
30-4 = 26 mph
convert to miles per second 26/3600 = .007222 miles/second
multiply that by 5 seconds gives you .03611miles convert that to feet gives you 190.6608 ft.