A certain map shows two roads. Road A is 1 and one fourth

Question

miles long but is 1 and seven eighths inches
long on the map. What is the unit rate for inches per mile on this map​? If road B is 6 miles ​long, how long is road B on the map​?
Question content area bottom
Part 1
The unit rate is
  
enter your response here inch​(es​) per mile.
​(Simplify your answer. Type an​ integer, fraction, or mixed​ number.)

Answer 1

To find the unit rate for inches per mile on the map, we need to first convert the length of Road A from miles to inches.

1. Convert miles to inches for Road A:

   • There are 63,360 inches in a mile.
   • Road A is \( 1 \frac{1}{4} \) miles long.

   To convert \( 1 \frac{1}{4} \) miles to an improper fraction: \[ 1 \frac{1}{4} = \frac{5}{4} \text{ miles} \]

   Now convert to inches: \[ \frac{5}{4} \text{ miles} \times 63,360 \text{ inches/mile} = \frac{5 \times 63,360}{4} = \frac{316,800}{4} = 79,200 \text{ inches} \]

2. Find the unit rate for inches per mile:

   • Length of Road A on the map: \( 1 \frac{7}{8} \) inches.
   • Convert \( 1 \frac{7}{8} \) inches to an improper fraction: \[ 1 \frac{7}{8} = \frac{15}{8} \text{ inches} \]

   Now, the unit rate can be calculated as: \[ \text{Unit rate (inches per mile)} = \frac{\text{Length on the map (inches)}}{\text{Actual length (miles)}} \] \[ \text{Unit rate} = \frac{\frac{15}{8}}{\frac{5}{4}} = \frac{15}{8} \times \frac{4}{5} = \frac{15 \times 4}{8 \times 5} = \frac{60}{40} = \frac{3}{2} \]

Thus, the unit rate is: \[ \frac{3}{2} \text{ inches per mile} \]

3. Calculate the length of Road B on the map:
   • Length of Road B: 6 miles.
   • Using the unit rate of \( \frac{3}{2} \) inches per mile, we can find the length on the map: \[ \text{Length on the map} = 6 \text{ miles} \times \frac{3}{2} \text{ inches/mile} = 6 \times \frac{3}{2} = 9 \text{ inches} \]

Final Answers:

• Unit rate: \( \frac{3}{2} \) inches per mile
• Length of Road B on the map: 9 inches