The distance $d$ a car travels varies directly as the time $t$. If the car travels $180km$ in $3$ hours, find how far it will travel in $5$ hours.

• A.
• B.
• C. $300\(\operatorname{\mathrm{km}\)}$
• D. $900\(\operatorname{\mathrm{km}\)}$

Answer: (C)

Verified step by step guidance

1. Recognize that the distance \( d \) varies directly as the time \( t \), which means the relationship can be written as \( d = kt \), where \( k \) is the constant of proportionality.
2. Use the given information that the car travels 180 km in 3 hours to find \( k \). Substitute \( d = 180 \) and \( t = 3 \) into the equation \( d = kt \) to get \( 180 = k \times 3 \).
3. Solve for \( k \) by dividing both sides of the equation by 3, resulting in \( k = \frac{180}{3} \).
4. Now that you have \( k \), use it to find the distance the car will travel in 5 hours by substituting \( t = 5 \) into the equation \( d = kt \).
5. Calculate \( d = k \times 5 \) to find the distance traveled in 5 hours (do not compute the final value here, just set up the expression).