Expressions Using Letter-Numbers | FIO

Question 12

A snail is trying to climb along the wall of a deep well. During the day it climbs up ‘u’ cm and during the night it slowly slips down ‘d’ cm. This happens for 10 days and 10 nights.

(a) Write an expression describing how far away the snail is from its starting position.

(b) What can we say about the snail’s movement if d > u?

Solution

We find the snail's net movement each day, then multiply by 10 days.

Step 1 — Net movement per day-night cycle

The snail climbs up 'u' cm during the day. It slips down 'd' cm during the night. Let us find the net change in position. This is for one full day and one full night.

Net movement = (climb up) - (slip down) $= u - d$

$\boxed{\mathbf{u - d \text{ cm}}}$

This is the distance covered in one cycle.

Step 2 — Total movement over 10 cycles

The snail repeats this for 10 days and 10 nights. So, there are 10 such day-night cycles. We multiply the net movement per cycle by 10. Let 'D' be the total distance from the start.

Total distance D = (net movement per cycle) $\times$ (number of cycles) $= (u - d) \times 10$ $= \mathbf{10(u - d)}$

$\boxed{\mathbf{10(u - d) \text{ cm}}}$

This is the expression for part (a).

Diagram 1

Step 3 — Movement when d > u

Now we consider what happens if 'd' is greater than 'u'. This means the slip down is more than the climb up. Let us look at the net movement per cycle. Net movement = $u - d$ . If $d > u$ , then $u - d$ will be a negative number. A negative value means the snail moves downwards. It moves away from its climbing goal. The snail is actually losing ground. It is getting further from the top. It is moving deeper into the well.

Answer

(a) The expression is $\mathbf{10(u - d) \text{ cm}}$ . (b) If $d > u$ , the snail moves downwards. It gets further from the top of the well. It moves deeper into the well.

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Q12

A snail is trying to climb along the wall of a deep well. During the day it climbs up ‘u’ cm and during the night it slowly slips down ‘d’ cm. This happens for 10 days and 10 nights.

(a) Write an expression describing how far away the snail is from its starting position.

(b) What can we say about the snail’s movement if d > u?

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