Interesting Burn / Rate Question

[Mr M]

Hey guys, my first post... here goes...

THE QUESTION IS

The amount of coal a train burns each mile is directly proportional to the speed at which it travels. How much coal will it burn on this particular 60 mile trip?

1) On a previous trip, the train burned 100 pounds of coal on a 60 mile trip at 60 miles per hour

2) On this particular trip, the train is travelling at a speed of 30 miles per hour.

[spoiler] Hey guys,

I just did this problem. Great question but I think that the answer is wrong.

See below...

THE QUESTION IS:

The amount of coal a train burns each mile is directly proportional to the speed at which it travels. How much coal will it burn on this particular 60 mile trip?

1) On a previous trip, the train burned 100 pounds of coal on a 60 mile trip at 60 miles per hour

2) On this particular trip, the train is travelling at a speed of 30 miles per hour.

[spoiler] The answer according to Veritas Prep is C (i.e. both together are needed).

My issue with this is that shouldn't A (or (1) above) be enough? My reasoning is below.

The question says that the burn per mile is directly proportional to the speed. HOWEVER, the TOTAL miles is 60 miles. Consequently, by my reasoning, irrespective of the speed, the same amount of coal should be burned at the end of a 60 mile journey. THIS IS BECAUSE LESS SPEED (and thus a lower burn rate) WILL BE COMPENSATED BY MORE TIME TRAVELING (thus a longer time burning).

For example, if burn is directly proportional to speed (as specified by the question), then at 30 miles an hour, the train burns half of what it would at 60 miles an hour. Now:
- At 60 miles per hour, the train burns 1 3/4 for every mile.
- At 30 miles per hour, the train burns 5/6 pounds of coal for every mile.
However, at a distance of 60 miles, amount of coal is burned is the same. I.e:
- At 5/6 pounds of coal every mile, at 60 miles at 30 miles an hour, 100 pounds of coal is burned.
- At 1 2/3 pounds of coal for every mile, at 60 miles at 60 miles per hour, 100 pounds of coal is burned.

THUS, either way, 100 pounds of coal is burned.

[/spoiler]

Could someone tell me why my reasoning above is incorrect?

[Morgoth]

The answer is correct. You need both the statements.

Statement 1 tells you the rate at which the coal burns, but does not tells you the speed of the train on this trip, it could be 60mph or 30mph or 5mph.

Statement 2 tells you only the speed of the train on this trip, but no relation between coal burning and speed. Insufficient.

Together they both tell you the speed of the train on this trip as well as the rate at which the coal burns.

[Ian Stewart]

The amount of coal a train burns each mile is directly proportional to the speed at which it travels. How much coal will it burn on this particular 60 mile trip?

1) On a previous trip, the train burned 100 pounds of coal on a 60 mile trip at 60 miles per hour

2) On this particular trip, the train is travelling at a speed of 30 miles per hour.

The answer according to Veritas Prep is C (i.e. both together are needed).

My issue with this is that shouldn't A (or (1) above) be enough? My reasoning is below.

The question says that the burn per mile is directly proportional to the speed. HOWEVER, the TOTAL miles is 60 miles. Consequently, by my reasoning, irrespective of the speed, the same amount of coal should be burned at the end of a 60 mile journey. THIS IS BECAUSE LESS SPEED (and thus a lower burn rate) WILL BE COMPENSATED BY MORE TIME TRAVELING (thus a longer time burning).

Your answer would be right (and the question would be more interesting) if the question said "The amount of coal a train burns each hour is directly proportional to the speed at which it travels." Then, as you say, any increase in speed would be compensated by the decrease in the time of the trip, and the answer would be A. However, as the question is worded, the answer is indeed C.