Question

Aubrey, running at a pace of 5 miles per hour, how many miles can she run in 90 minutes?

Answer 1

Hint: In the question, we have given the speed of Aubrey as 5 miles per hour and we have to find the miles that she runs in 90 minutes. To solve this problem, we are going to use the formula of speed, distance and time which is given by $Speed=\dfrac{Dis\tan ce}{Time}$.Now, we have given speed equal to 5 miles per hour and time equal to 90 minutes as speed is given in miles per hour so we have to convert 90 minutes to hour which will be 1.5 hours. Now, put the time equal to 1.5 hours and speed equal to 5 miles per hour in the formula, we will get the distance in miles.

Complete step-by-step answer:
In the question given above, we have given the speed at which Aubrey runs i.e. 5 miles per hour and we have to find the distance in miles that she can run in 90 minutes.
We know the relation between distance, speed and time as:
$Speed=\dfrac{Dis\tan ce}{Time}$…………. Eq. (1)
From the question, we know the speed equal to 5 miles per hour and the time equal to 90 minutes and need to find the distance in miles. As the speed is given in miles per hour so we have to convert the time in minutes to hour.
Converting 90 minutes to hour we get,
$\begin{align}
  & 1hour=60\min utes \\
 & \Rightarrow 1\min ute=\dfrac{1}{60}hour \\
 & \Rightarrow 90\min utes=\dfrac{90}{60}hours=\dfrac{3}{2}hours \\
\end{align}$
From the above conversion, we have found that 90 minutes is equal to $\dfrac{3}{2}$ hours or 1.5 hours.
Now, substituting the value of speed as 5 miles per hour and time equal to 1.5 hours in eq. (1) we will get the distance run by Aubrey in miles as follows:
$\begin{align}
  & Speed=\dfrac{Dis\tan ce}{Time} \\
 & \Rightarrow 5=\dfrac{Dis\tan ce}{1.5} \\
\end{align}$
 In the above equation, cross-multiplication will give:
$\begin{align}
  & 5\left( 1.5 \right)=Dis\tan ce \\
 & \Rightarrow Dis\tan ce=7.5miles \\
\end{align}$
From the above solution, we have found that Aubrey ran 7.5 miles in 90 minutes.
Hence, Aubrey runs 7.5 miles in 90 minutes at a pace of 5 miles per hour.

Note: The possible mistake that could happen while solving the above problem is that you might forget to convert 90 minutes in hours and then solve the question.
The easiest way to counter this mistake is to always check the given units of speed and then accordingly convert the units of distance and time whenever required.