Solve 1/42t+1/38t=1+1/22*1/8

$$\frac { 1 } { 42 } t + \frac { 1 } { 38 } t = 1 + \frac { 1 } { 22 } \cdot \frac { 1 } { 8 }$$

Solve for t

$$t = \frac{70623}{3520} = 20\frac{223}{3520} \approx 20.063352273$$

Steps for Solving Linear Equation

Combine \frac{1}{42}t and \frac{1}{38}t to get \frac{20}{399}t.

$$\frac{20}{399}t=1+\frac{1}{22}\times \frac{1}{8}$$

Multiply \frac{1}{22} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20}{399}t=1+\frac{1\times 1}{22\times 8}$$

Do the multiplications in the fraction \frac{1\times 1}{22\times 8}.

$$\frac{20}{399}t=1+\frac{1}{176}$$

Convert 1 to fraction \frac{176}{176}.

$$\frac{20}{399}t=\frac{176}{176}+\frac{1}{176}$$

Since \frac{176}{176} and \frac{1}{176} have the same denominator, add them by adding their numerators.

$$\frac{20}{399}t=\frac{176+1}{176}$$

Add 176 and 1 to get 177.

$$\frac{20}{399}t=\frac{177}{176}$$

Multiply both sides by \frac{399}{20}, the reciprocal of \frac{20}{399}.

$$t=\frac{177}{176}\times \frac{399}{20}$$

Multiply \frac{177}{176} times \frac{399}{20} by multiplying numerator times numerator and denominator times denominator.

$$t=\frac{177\times 399}{176\times 20}$$

Do the multiplications in the fraction \frac{177\times 399}{176\times 20}.

$$t=\frac{70623}{3520}$$