The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 4h \)
100 miles

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 5}{9 x 5} \) - \( \frac{5 x 3}{15 x 3} \)

\( \frac{35}{45} \) - \( \frac{15}{45} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{35 - 15}{45} \) = \( \frac{20}{45} \) = \(\frac{4}{9}\)

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{80mi}{40mph} \)
2 hours