"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,
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