Question

1. jeff knows that his semi - trailer truck is 3.2 m high. a tunnel is marked as \max height: 10 6\ \. will jeffs truck fit through the tunnel?
2. benjamin owns an older american truck. the odometer shows distance travelled in miles. on a recent trip to deliver produce for his employer, he drove 1564 mi. his employer pays him $0.89/km for the use of his own truck. how much will he be reimbursed for the use of his truck for the trip?
3. your learner’s permit says you are 160 cm tall. how tall are you in imperial?

Explanation:

Problem 9 (Jeff's Truck and Tunnel)

Step1: Convert tunnel height to meters

1 foot = 0.3048 meters, 1 inch = 0.0254 meters.
Tunnel height: \( 10'6'' = 10 \times 0.3048 + 6 \times 0.0254 \)
\( = 3.048 + 0.1524 = 3.2004 \, \text{m} \)

Step2: Compare truck and tunnel height

Truck height: \( 3.2 \, \text{m} \)
Tunnel height: \( 3.2004 \, \text{m} \)
Since \( 3.2 < 3.2004 \), the truck fits.

Step1: Convert miles to kilometers

1 mile = 1.60934 kilometers.
Distance in km: \( 1564 \times 1.60934 \approx 1564 \times 1.60934 \approx 2517.01 \, \text{km} \)

Step2: Calculate reimbursement

Reimbursement = Rate × Distance
\( = 0.89 \times 2517.01 \approx 2240.14 \)

Step1: Convert centimeters to inches (or feet + inches)

1 inch = 2.54 cm.
Height in inches: \( \frac{160}{2.54} \approx 62.99 \, \text{inches} \)

Step2: Convert inches to feet + inches

1 foot = 12 inches.
Feet: \( \lfloor \frac{62.99}{12}
floor = 5 \) (feet)
Inches: \( 62.99 - 5 \times 12 = 2.99 \approx 3 \) (inches)
So, \( 5'3'' \) (or \( 62.99'' \) if in inches).

Answer:

Yes, Jeff's truck will fit through the tunnel.

Problem 10 (Benjamin's Reimbursement)