X.

3. A dog makes $4$ leaps while a rabbit makes $5$; but $3$ of the dog's leaps are equivalent to $4$ of the rabbit's. The rabbit has a start of $90$ of the dog's leaps. How many leaps will each take before the rabbit is caught?

Exercise 62.

Ex. Find the time between $2$ and $3$ o'clock when the hands of a clock are together.

At 2 o'clock the hour-hand is 10 minute-spaces ahead of the minute-hand.

lint Let x = the number of spaces the minute-hand moves over. lint Then x - 10 = the number of spaces the hour-hand moves over. [1] Now, as the minute-hand moves $12$ times as fast as the hour-hand, $12(x-10)$ = the number of spaces the minute-hand moves over.

Therefore the time is $10\frac{10}{11}$ minutes past $2$ o'clock.

1. Find the time between $5$ and $6$ o'clock when the hands of a clock are together.

2. Find the time between $2$ and $3$ o'clock when the hands of a clock are at right angles to each other.

In this case the minute-hand is $15$ minutes ahead of the hour-hand.

3. Find the time between $2$ and $3$ o'clock when the hands of a clock point in opposite directions.

In this case the minute-hand is $30$ minutes ahead of the hour-hand.

4. Find the time between $1$ and $2$ o'clock when the hands of a clock are at right angles to each other.

5. Find the time between $1$ and $2$ o'clock when the hands of a clock point in opposite directions.

6. At what time between $7$ and $8$ o'clock are the hands of a watch together?

Exercise 63.

Ex. A rectangle has its length $6$ feet more and its width $5$ feet less than the side of its equivalent square. Find the dimensions of the rectangle.

lint Let x = the number of feet in a side of the square. lint Then x + 6 = the number of feet in the length of the rectangle, lintand x - 5 = the number of feet in the width of the rectangle. Since the area of a rectangle is equal to the product of the number of units of length in the length and width of the rectangle, $(x+6)(x-5)$ = the area of the rectangle in square feet, lintand x × x = the area of the square in square feet.

But these areas are equal.

Therefore the dimensions of the rectangle are $36$ feet and $25$ feet.

1. A rectangle has its length and breadth respectively $7$ feet longer and $6$ feet shorter than the side of the equivalent square. Find its area.