The distance of Brandon’s bike in each interval of time can be represented in the attached Table 1.
Further explanation:
Given:
Brandon enters in to the bike race and he bikes \(8\frac{1}{2}\text{ miles}\) in every \(\frac{1}{2}\text{ hour}\).
Calculation:
It is given that in every \(\frac{1}{2}\text{ hour}\) Brandon bikes \(8\frac{1}{2}\text{ miles}\).
The distance \(8\frac{1}{2}\text{ miles}\) is in the form of mixed fraction.
Therefore, the distance \(8\frac{1}{2}\text{ miles}\) can be written in the form of decimal as follows:
\(\boxed{8\frac{1}{2}\text{ miles}\rightarrow8.5\text{ miles}}\)
Brandon bike's \(8.5\text{ miles}\) in every \(\frac{1}{2}\text{ hour}\).
We know that \(1\text{ hour}\) is equivalent to \(60\text{ minutes}\).
So, \(0.5\text{ hour}\) can be converted into minutes as follows:
\(\boxed{\begin{aligned}1\text{ hour}\rightarrow60\text{ minutes}\\0.5\text{ hour}\rightarrow30\text{ minutes}\end{aligned}}\)
Therefore, in every \(30\text{ minutes}\) Brandon bikes \(8.5\text{ miles}\).
So, in next \(30\text{ minutes}\) Brandon also bikes \(8.5\text{ miles}\).
In every \(1\text{ hour}\) Brandon travels \(\boxed{8.5+8.5=17\text{ miles}}\).
In every \(1:30\text{ hour}\) Brandon travels \(\boxed{17+8.5=25.5\text{ miles}}\).
Method 2:
Speed of Brandon’s bike can be calculated as ,
\(\boxed{\text{Speed}=\dfrac{d}{t}}\) …… (1)
Here, \(d\) is the distance and \(t\) is the time.
The distance is \(8.5\text{ miles}\) and time is \(0.5\text{ hour}\).
Now, substitute \(d=8.5\) and \(t=0.5\) in the equation (1) to obtain the speed as follows:
\(\begin{aligned}\text{Speed}&=\dfrac{8.5}{0.5}\\&=17\text{ miles per hour}\end{aligned}\)
Therefore, the rate of travelling of Brandon’s bike is \(17\text{ miles per hour}\).
The distance of Brandon’s bike in each interval of time can be represented in the attached Table 1.
Learn more:
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Speed, time and distance
Keywords: Distance, Brandon’s bike, interval, time, race, mixed fraction, distance, decimal, hour, minutes, rate, fraction, velocity, 1/2 miles, 1/2 hour.
