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. Identify the direct variation relationship between distance \(d\) and time \(t\). This means we can write the equation as \(d = k \times t\), where \(k\) is the constant of proportionality.
2. Use the given information that the car travels 180 km in 3 hours to find the constant \(k\). Substitute \(d = 180\) and \(t = 3\) into the equation: \(180 = k \times 3\).
3. Solve for \(k\) by dividing both sides of the equation by 3: \(k = \frac{180}{3}\).
4. Now that you have the value of \(k\), use it to find the distance traveled in 5 hours by substituting \(t = 5\) into the direct variation formula: \(d = k \times 5\).
5. Multiply the constant \(k\) by 5 to find the distance \(d\) the car will travel in 5 hours.