Questions: How many minutes (min) will it take for a car that is moving at 5.4 × 10 mi / h to travel 250. km?

How many minutes (min) will it take for a car that is moving at 5.4 × 10 mi / h to travel 250. km?
Transcript text: How many minutes $(\min )$ will it take for a car that is moving at $5.4 \times 10 \mathrm{mi} / \mathrm{h}$ to travel 250. km?
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Solution

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Solution Steps

Step 1: Convert Speed from Miles per Hour to Kilometers per Hour

The speed of the car is given as \(5.4 \times 10 \, \text{mi/h}\). First, convert this speed to kilometers per hour using the conversion factor \(1 \, \text{mi} = 1.60934 \, \text{km}\).

\[ 5.4 \times 10 \, \text{mi/h} = 54 \, \text{mi/h} \]

\[ 54 \, \text{mi/h} \times 1.60934 \, \text{km/mi} = 86.1044 \, \text{km/h} \]

Step 2: Convert Distance from Kilometers to Miles

The distance to be traveled is 250 km. Convert this distance to miles using the conversion factor \(1 \, \text{mi} = 1.60934 \, \text{km}\).

\[ 250 \, \text{km} \times \frac{1 \, \text{mi}}{1.60934 \, \text{km}} \approx 155.343 \, \text{mi} \]

Step 3: Calculate Time in Hours

Calculate the time it takes to travel 155.343 miles at a speed of 54 mi/h.

\[ \text{Time in hours} = \frac{155.343 \, \text{mi}}{54 \, \text{mi/h}} \approx 2.8758 \, \text{hours} \]

Step 4: Convert Time from Hours to Minutes

Convert the time from hours to minutes.

\[ 2.8758 \, \text{hours} \times 60 \, \text{minutes/hour} = 172.548 \, \text{minutes} \]

Final Answer

The time it will take for the car to travel 250 km is approximately \(\boxed{172.548 \, \text{minutes}}\).

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