Solve for T in the equation T = 1 / (1/5 + 1/3 of 2 1/4 10/39 x 1 2/11). 2. A motorist travelling at a steady speed of 120 km/h covers a section. Travelling at the n minimize accidents a speed limit is imposed. takes 5 minutes longer to cover the same section. Calculate the

First, convert the mixed fractions to improper fractions and perform the multiplication ("of" means multiplication).
$1\frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}$
$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$
Numerator:

$$\frac{9}{5} \times \frac{7}{3} = \frac{3 \times 3}{5} \times \frac{7}{3} = \frac{3 \times 7}{5} = \frac{21}{5}$$

First, perform the multiplication, then the addition.
Convert the mixed fraction to an improper fraction:
$1\frac{2}{11} = \frac{1 \times 11 + 2}{11} = \frac{13}{11}$
Multiplication term:

$$\frac{2}{39} \times \frac{13}{11} = \frac{2}{3 \times 13} \times \frac{13}{11} = \frac{2}{3 \times 11} = \frac{2}{33}$$

Now, add this to $\frac{5}{6}$:

$$\frac{5}{6} + \frac{2}{33}$$

Find the least common multiple (LCM) of 6 and 33, which is 66.

$$\frac{5 \times 11}{6 \times 11} + \frac{2 \times 2}{33 \times 2} = \frac{55}{66} + \frac{4}{66} = \frac{59}{66}$$

Now substitute the simplified numerator and denominator back into the original equation:

$$\frac{1}{T} = \frac{\frac{21}{5}}{\frac{59}{66}}$$

To divide by a fraction, multiply by its reciprocal:

$$\frac{1}{T} = \frac{21}{5} \times \frac{66}{59}$$ $$\frac{1}{T} = \frac{21 \times 66}{5 \times 59}$$ $$\frac{1}{T} = \frac{1386}{295}$$

To find T, take the reciprocal of both sides of the equation:

$$T = \frac{295}{1386}$$

The value of T is:

$$\frac{295}{1386}$$