Fifi stared. "Why--how in the world, Mr Queed--"

"Let us see if I am right. Proceed. Read me what you have written down."

"Let _x_ equal the number of rods he built each day," began Fifi bravely.

"Proceed."

"Then _105_ divided by _x_ equals number of days consumed. And _105_ divided by _x - 2_ equals number of days consumed, if he had built _2_ rods less a day."

"Of course."

"And (_105_ _x - 2_) + _6_ = number of days consumed if it had taken him six days longer."

"Nothing of the sort."

Fifi coughed. "I don't see why, exactly."

"When the text says 'six days longer,' it means longer than what?"

"Why--longer than ever."

"Doubtless. But you must state it in terms of the problem."

"In terms of the problem," murmured Fifi, her red-brown head bowed over the bewildering book--"in terms of the problem."

"Of course," said her teacher, "there is but one thing which longer can mean; that is longer than the original rate of progress. Yet you add the six to the time required under the new rate of progress."

"I--I'm really afraid I don't quite see. I'm dreadfully stupid, I know--"

"Take it this way then. You have set down here two facts. One fact is the number of days necessary under the old rate of progress; the other is the number of days necessary under the new rate. Now what is the difference between them?"

"Why--isn't that just what I don't know?"

"I can't say what you don't know. This is something that _I_ know very well."

"But you know everything," she murmured.

Without seeking to deny this, Queed said: "It tells you right there in the book."

"I don't see it," said Fifi, nervously looking high and low, not only in the book but all over the room.

The young man fell back on the inductive method: "What is that six then?"

"Oh! _Now_ I see. It's the difference in the number of days consumed--isn't it?"

"Naturally. Now put down your equation. No, no! The greater the rate of progress, the fewer the number of days. Do not attempt to subtract the greater from the less."

Now Fifi figured swimmingly:--

(105/(x-2)) - (105/x) = 6

105x - 105x + 210 = 6x^2 - 12x

6x^2 - 12x - 210 = 0

6x^2 - 12x - 210 = 0

x^2 - 2x - 35 = 0

(x - 7) (X + 5) = 0

x = 7 or -5

She smiled straight into his eyes, sweetly and fearlessly. "Seven! Just what you said! Oh, if I could only do them like you! I'm ever and ever so much obliged, Mr. Queed--and now I can go to bed."

Mr. Queed avoided Fifi's smile; he obviously deliberated.

"If you have any more of these terrible difficulties," he said slowly, "it isn't necessary for you to sit there all evening and cry over them.

You ... may ask me to show you."

"Oh, _could_ I really! Thank you ever so much. But no, I won't be here, you see. I didn't mean to come to-night--truly, Mr. Queed--I know I bother you _so_--only Mother made me."

"Your mother made you? Why?"

"Well--it's right cold upstairs, you know," said Fifi, gathering up her books, "and she thought it might not be very good for my cough...."

Queed glanced impatiently at the girl's delicate face. A frown deepened on his brow; he cleared his throat with annoyance.

"Oh, I am willing," he said testily, "for you to bring your work here whenever it is very cold upstairs."

"Oh, how good you are, Mr. Queed!" cried Fifi, staggered by his n.o.bility. "But of course I can't think of bothering--"

"I should not have asked you," he interrupted her, irritably, "if I had not been willing for you to come."

But for all boarders, their comfort and convenience, Fifi had the great respect which all of us feel for the source of our livelihood; and, stammering grateful thanks, she again a.s.sured him that she could not make such a nuisance of herself. However, of course Mr. Queed had his way, as he always did.

This point definitely settled, he picked up his pencil, which was his way of saying, "And now, for heaven's sake--good-night!" But Fifi, her heart much softened toward him, stood her ground, the pile of school-books tucked under her arm.

"Mr. Queed--I--wonder if you won't let me get something to put on your forehead? That bruise is so dreadful--"

"Oh, no! No! It's of no consequence whatever."

"But I don't think you can have noticed how bad it is. Please let me, Mr. Queed. Just a little dab of arnica or witch-hazel--"

"My forehead does very well as it is, I a.s.sure you."

Fifi turned reluctantly. "Indeed something on it would make it get well so _much_ faster. I wish you would--"