An Indy 500 car can travel 111 m/s. What is the speed of the car in miles per hour? Given: 1 mi = 1.61 km and 1 h = 3600 s. How do you solve
The Correct Answer and Explanation is:
To convert the speed of the Indy 500 car from meters per second (m/s) to miles per hour (mph), follow these steps:
Step 1: Convert meters to kilometers
First, we need to convert the given speed in meters per second (m/s) into kilometers per second (km/s). We know that:1 km=1000 m1 \, \text{km} = 1000 \, \text{m}1km=1000m
So, to convert 111 m/s to km/s:111 m/s×1 km1000 m=0.111 km/s111 \, \text{m/s} \times \frac{1 \, \text{km}}{1000 \, \text{m}} = 0.111 \, \text{km/s}111m/s×1000m1km=0.111km/s
Step 2: Convert seconds to hours
Next, we need to convert the time from seconds to hours. There are 3600 seconds in one hour (1 h = 3600 s). So, to convert 0.111 km/s to km/h:0.111 km/s×3600 s/h=399.6 km/h0.111 \, \text{km/s} \times 3600 \, \text{s/h} = 399.6 \, \text{km/h}0.111km/s×3600s/h=399.6km/h
Step 3: Convert kilometers to miles
Now, we need to convert kilometers per hour (km/h) to miles per hour (mph). We’re given the conversion factor:1 mile=1.61 km1 \, \text{mile} = 1.61 \, \text{km}1mile=1.61km
So, to convert 399.6 km/h to mph:399.6 km/h×1 mile1.61 km=248.5 mph399.6 \, \text{km/h} \times \frac{1 \, \text{mile}}{1.61 \, \text{km}} = 248.5 \, \text{mph}399.6km/h×1.61km1mile=248.5mph
Final Answer
The speed of the Indy 500 car is approximately 248.5 miles per hour.
Explanation
This process involves three main unit conversions: from meters to kilometers, from seconds to hours, and from kilometers to miles. The key to solving this problem is setting up each conversion step carefully and ensuring that the units cancel correctly.
