Great work on POTW #23. Many students obtained the correct ages of 7, 11, and 23. Funny coincidence that this last number was also the POTW number.
Please see the latest POTW #24 below. Can you use algebra to solve it? What other methods might you use?
The train is going 36km per hour. It takes the train 30 seconds to be completely in the tunnel (1km). Now to get the km per hour, you first multiply 30x2(minute) to get 60 and multiply that by 60 (hour) again to get 36km per hour
ReplyDeleteWhen the trains last car has just completely entered the tunnel the train's front is 1000 m in the tunnel as it has a length of 1000 m. When the train's front emerges the other end, it's front is 3000 m in the tunnel as the tunnel is 3000 m long.
ReplyDelete3000-1000=2000
Therefore, the train travels a total distance of 2000 m in 30 seconds.
If the train travels 2000 m in 30 seconds it has to travel an x amount in 3600 seconds (in one hour).
Therefore, x= 2000 x 3600 /30=240 000 m which is 240 km (240000/1000)
Thus, the speed of the train is 240 km/h.
Heres how I solved it:
ReplyDeleteSo the the 1000m long train travels through a 3000m long tunnel, So no matter what (since this train is 1000m long) when the back of the train enters the tunnel the front part would have been 1000m into the tunnel already, and in the time span of 30 seconds the front part of the train emerges from the tunnel and the back is 2000m in.
This means the train moved 2000m in 30 seconds (from the start of the tunnel to 2000m in is 2000m). This means the train is going at 4000m per minute, but we're trying to find the kilometers in an hour so you would times that by 60 because there is 60 minutes in an hour. You will get 240000m/hr but since we need in kilometres we convert that into kilometers and get: 240km/hr
This train is moving at 240km/hr
1000 meters -> 1 kilometer
ReplyDelete3000 meters -> 3 kilometers
Ratio = 3 kilometers/30 seconds
30 seconds * 60 = 1800 seconds
1800 seconds * 2 = 3600 seconds or 1 hour
3 kilometers * 60 = 180
180 * 2 = 360 kilometers
New Ratio : 360 km/hr
30sec from complete tunnel entry to partial exit
ReplyDeletetrain = 1000m = 1km
tunnel = 3000m = 3km
3km - 1km = 2km
train travels 2km in 30sec
3600sec = 1h
30x=3600
X = 120sec
2km * 120sec = 240km/h
The Train Is Traveling at 240km/h
I got 240 miles as my answer, hard copy.
ReplyDeleteThe train completely enters the tunnel at 1km meaning it travels 2km in the next 30 secs. That means that means ti travels at a rate of 200m/3sec.
ReplyDelete(200m/3)20= 4km/1min
(4km/1min)60 = 240km/hr
Therefore the speed at which the train travels at is 240km/hr
I did it hard copy
ReplyDeleteSince the time starts when the train is already 1000m in the tunnel it has 2000m left so it takes 30s to travel 2km (1000m=1km). The ratio is 2km/30s. The questions specifies in an hour, so I need to find out how many time 30s goes in an hour. 3600/30= 120. Then I multiply 2km by the number of times 30s goes in 1h. 2*120= 240.
ReplyDeleteThe train travels at a speed of 240km/hr.
The train is travelling at a speed of 240km/hour.
ReplyDeleteOnce the end of the train enter the 3000m tunnel, the front of the train is already 1000m into the tunnel. That means only 2000m of the tunnel still needs to be travelled. That means it takes 30 seconds for the front of the train to travel 2000m as it takes 30 seconds from the time the last car enters (engine is 1000m into the tunnel) until the engine appears at the other end. So here are the numbers:
In 30 seconds: 2000m/30 secs
In 1 minute: 4000m/1 min
30 secs*2= 60 secs or 1 min
2000m*2= 4000m
In 1 hour: 24000m/1 hour
1 min*60= 60 mins or 1 hour
4000m*60= 24000m
In 1 hour in km: 24km/1 hour
1000m=1km
24000km=24km
So first we know that the train has already covered 1000m of this 3000m tunnel. 3000-1000=2000. So now we know that the train has 30s to travel 2000m. Now we need to find how many seconds are in 1 hour. There are 3600. Now we do 3600/30 to get 120. Then I convert the 2000m to km which is 2km. Then I multiplied 120 by 2 to get 240. Therefore, the train travels at 240km/h.
ReplyDelete