A footbridge is 5 feet wide and is built with wood planks that are 6 inches wide. How many planks wide is the path?
The correct answer and explanation is:
Let’s solve this step-by-step:
Problem:
- The footbridge is 5 feet wide.
- Each plank is 6 inches wide.
- How many planks wide is the path?
Step 1: Convert all measurements to the same unit.
Since the width of the footbridge is given in feet and the plank width is given in inches, it’s easier to convert everything to inches.
- 1 foot = 12 inches
- Width of footbridge = 5 feet = 5 × 12 = 60 inches
Step 2: Determine how many planks fit in 60 inches.
Each plank is 6 inches wide. To find how many planks fit into 60 inches, divide the total width of the bridge by the width of each plank: Number of planks=Width of bridge in inchesWidth of each plank in inches=606=10\text{Number of planks} = \frac{\text{Width of bridge in inches}}{\text{Width of each plank in inches}} = \frac{60}{6} = 10
Final Answer:
The footbridge is 10 planks wide.
Explanation (300 words):
When working with measurements, it’s important to keep units consistent. In this problem, the footbridge width is given in feet, while the plank width is given in inches. To accurately calculate how many planks are needed to cover the width of the bridge, we first convert the bridge width from feet to inches.
Since 1 foot equals 12 inches, the bridge width of 5 feet translates to 60 inches (5 × 12 = 60). Now, both measurements are in inches, making it straightforward to compare.
Next, we take the width of each plank, which is 6 inches, and divide the total bridge width (60 inches) by the plank width (6 inches). The result, 10, tells us how many planks fit side-by-side to span the full width of the footbridge.
This calculation assumes the planks are laid edge to edge without gaps. If gaps were present or the planks were irregularly sized, the number could differ slightly. However, based on the problem’s straightforward wording, 10 planks fit perfectly across.
Understanding unit conversion is crucial for such problems. Converting feet to inches avoided errors in the calculation. Without conversion, one might mistakenly divide 5 by 6, which would give a misleading answer since the units wouldn’t be comparable.
In real-world applications, such calculations help carpenters, builders, and designers plan materials needed to construct paths, decks, or bridges, ensuring accurate budgeting and material ordering. Knowing exactly how many planks fit into a certain width prevents waste and helps estimate costs more precisely.