We are asked to find the average speed of the record winner of the Boston Marathon's wheelchair division. We know that the Boston Marathon is 26.2 miles long and the record is 1 hour, 18 minutes, and 27 seconds. Let's start by writing a rate to show this situation.
26.2 mi/1h 18 min 27 s
To find the speed, we will write an equivalent rate with a denominator of 1 hour. Before we do this, we will convert the time to hours. Recall that 1h=60 minutes. Therefore, to convert 18 minutes to hours, we will multiply it by the ratio 1h60min. We will use this ratio because it allows us to cancel out the common factors.
We found that 18 minutes is equal to 0.3 hour and 27 seconds is equal to 0.0075 hour. Now we can rewrite the rate so that the denominator is expressed in hours.
26.2 mi/1h 18 min 27 s = 26.2 mi/1h + 0.3 h + 0.0075 h
Now we will calculate the unit rate. To do so, we need to write an equivalent rate with a denominator of 1 hour. For simplicity, let's ignore the units.
We found the unit rate!
26.2 mi/1h 18 min 27 s ≈ 20.04 mi/1h
As we can see, the unit rate is about 20.04mi1h. This means that the average speed of the record winner is about 20.04 miles per hour.
We want to find about how long it would take the record winner to complete a 30-mile race. We will do this by using the average speed that we found in Part A. Recall that the speed of a moving object is calculated by dividing the distance traveled by the amount of time spent traveling.
Speed = Distance traveled/Time interval
We can use this formula to calculate the amount of time spent traveling if we are given the speed and distance.
Time interval = Distance traveled/Speed
In this case, the speed is about 20.04 miles per hour and the distance is 30 miles. Let's substitute these values into the formula for the time interval.
Time interval = 30 mi/20.04 mih
Now we can calculate the quotient. For simplicity, we will ignore the units. Since the distance is expressed in miles and the speed is expressed in miles per hour, we will get the time interval in hours.
