t60+t65=1

To write t60 as a fraction with a common denominator, multiply by 1313.

t60⋅1313+t65=1

To write t65 as a fraction with a common denominator, multiply by 1212.

t60⋅1313+t65⋅1212=1

Write each expression with a common denominator of 780, by multiplying each by an appropriate factor of 1.

Multiply t60 and 1313.

t⋅1360⋅13+t65⋅1212=1

Multiply 60 by 13.

t⋅13780+t65⋅1212=1

Multiply t65 and 1212.

t⋅13780+t⋅1265⋅12=1

Multiply 65 by 12.

t⋅13780+t⋅12780=1

t⋅13780+t⋅12780=1

Combine the numerators over the common denominator.

t⋅13+t⋅12780=1

Simplify the numerator.

Move 13 to the left of t.

13⋅t+t⋅12780=1

Move 12 to the left of t.

13t+12⋅t780=1

Add 13t and 12t.

25t780=1

25t780=1

Cancel the common factor of 25 and 780.

Factor 5 out of 25t.

5(5t)780=1

Cancel the common factors.

Factor 5 out of 780.

5(5t)5(156)=1

Cancel the common factor.

5(5t)5⋅156=1

Rewrite the expression.

5t156=1

5t156=1

5t156=1

5t156=1

Graph each side of the equation. The solution is the x-value of the point of intersection.

t≈31.2

Solve Graphically t/60+t/65=1