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Maths-

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Question

For gym class, Shayla completed a 4-mile walking and running exercise. She ran for 7t miles and she walked for $3 open parentheses 13 over 15 minus t close parentheses$ miles, where t is the total amount of time, in hours, Shayla spent running. The equation $7 t plus 3 open parentheses 13 over 15 minus t close parentheses equals 4$ models this situation
What is the value of t in the equation that models this situation?

$\frac{7}{50}$
$\frac{7}{20}$
$\frac{31}{60}$
$\frac{13}{15}$

The correct answer is: $7 over 20$

Hint:

○        The concept used in this question is of knowledge of algebraic equations.
○        Correct interpretation of given information is necessary.
○        Concept of speed should be known.
○     Speed = Distance   time
Step by step explanation:
Given:
Equation: $7 t plus 3 open parentheses 13 over 15 minus t close parentheses equals 4$
Step 1:
Simplify the equation.
$7 t plus 3 open parentheses 13 over 15 minus t close parentheses equals 4$
$not stretchy rightwards double arrow 7 t plus 39 over 15 minus 3 t equals 4$
$not stretchy rightwards double arrow 4 straight t plus 39 over 15 equals 4$
Step 2:
Seperate term with variable on one side and without variable on another side.
$not stretchy rightwards double arrow 4 straight t equals 4 minus 39 over 15$
$not stretchy rightwards double arrow 4 straight t equals fraction numerator left parenthesis 15 cross times 4 right parenthesis minus 39 over denominator 15 end fraction$
$not stretchy rightwards double arrow 4 t equals fraction numerator 60 minus 39 over denominator 15 end fraction$
$not stretchy rightwards double arrow 4 straight t equals 21 over 15$
$not stretchy rightwards double arrow straight t equals fraction numerator 21 over denominator 15 cross times 4 end fraction$
$not stretchy rightwards double arrow straight t equals 21 over 60$
Step 3:
Simplify the $21 over 60$
We will get,
$not stretchy rightwards double arrow straight t equals fraction numerator 21 divided by 3 over denominator 60 divided by 3 end fraction$
$not stretchy rightwards double arrow straight t equals 7 over 20$
∴ t = $7 over 20$
Hence, value of t is $7 over 20$ .

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