Discussion
A train of length l, traveling at a constant velocity, passes a pole in t seconds. If the same train traveling at the same velocity passes a platform in 3t seconds, then the length of the platform is
*This question is included in Nova Math - Problem Set X: Word Problems, question #24
| (A) | 0.5l |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 11/07/2012 09:17
Why is the length of the plataforma l+x and not just x?
Posted: 01/07/2013 19:19
Daniela, this is because it assumes when the train "passes the platform" it means the train's tail has left the platform, whereas our post only considered the head of the train has left the platform. We admit that the writer's explanation makes more sense than his.
Time to pass the platform = 3t;
velocity * time = length of platform + length of train;
l / t * 3t = x + l;
3l = x + l;
x = 2l.
Time to pass the platform = 3t;
velocity * time = length of platform + length of train;
l / t * 3t = x + l;
3l = x + l;
x = 2l.
Posted: 11/13/2012 00:51
Daniela, let's try to explain in simpler terms. Recall that velocity is the rate at which distance is traveled in time units. To know the length of the platform (distance), since we are given the time (3t seconds), we need to know the velocity of the train.
Well, the velocity of the train can be calculated from the first hint. The whole length of the train (l) is traveled entirely within time t. So the velocity = l / t.
That means the length of the platform is velocity * time = l / t * 3t = 3l.
Well, the velocity of the train can be calculated from the first hint. The whole length of the train (l) is traveled entirely within time t. So the velocity = l / t.
That means the length of the platform is velocity * time = l / t * 3t = 3l.
Posted: 01/07/2013 17:38
Format on answer is cut off
Posted: 01/07/2013 19:08
Justin, here is the correction:
The distance traveled by the train while passing the pole is l (which is the length of the train). The train takes t seconds to pass the pole. Recall the formula velocity = distance/time.
Applying this formula, we get
velocity = l/t
While passing the platform, the train travels a distance of l + x, where x is the length of the platform. The train takes 3t seconds at the velocity of l/t to cross the platform. Recalling the formula distance = velocity × time and substituting the values for the respective variables, we get
l + x = l/t * 3x
l + x = 3l
x = 2l
Hence, the length of the platform is 2l. The answer is (D).
The distance traveled by the train while passing the pole is l (which is the length of the train). The train takes t seconds to pass the pole. Recall the formula velocity = distance/time.
Applying this formula, we get
velocity = l/t
While passing the platform, the train travels a distance of l + x, where x is the length of the platform. The train takes 3t seconds at the velocity of l/t to cross the platform. Recalling the formula distance = velocity × time and substituting the values for the respective variables, we get
l + x = l/t * 3x
l + x = 3l
x = 2l
Hence, the length of the platform is 2l. The answer is (D).