A cyclist rode for 3.5 hours and completed a distance of 60.9 miles. if she kept the same average speed for each hour, how far did she ride in 1 hour?

estimate the quotient. include an equation to show your work. explain your thinking

1 answer

To find out how far the cyclist rode in 1 hour, we need to calculate her average speed. We can do this by dividing the total distance she rode by the total time she rode.

Equation: \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \] Inserting the values we have: \[ \text{Average Speed} = \frac{60.9 \text{ miles}}{3.5 \text{ hours}} \]

Now, let’s calculate this value. We can estimate the quotient by simplifying the values.

First, we can round the numbers to make the division easier:

  • \(60.9\) can be rounded to \(61\)
  • \(3.5\) can be approximately \(3.5\) for more precise calculations but can be thought of as \(3.5\) being close to \(3\) for simpler estimating.
  1. If we divide \(61\) by \(3.5\), let's convert \(3.5\) to a whole number for ease:
    • \(3.5 = \frac{7}{2}\), which means we can multiply \(61\) by \(2\) to make the denominator a whole number. \[ 61 \div 3.5 = 61 \times \frac{2}{2 \div 1} = \frac{122}{7} \]

Next, we estimate \(122 \div 7\):

  • \(7\) goes into \(12\) once, subtracting gives \(5\), bringing down the \(2\) gives \(52\).
  • \(7\) goes into \(52\) seven times (since \(7 \times 7 = 49\)), subtracting gives \(3\), bringing down leads to \(30\).
  • \(7\) goes into \(30\) four times (since \(7 \times 4 = 28\)), leaving us with \(2\).

So, \(122 \div 7\) is approximately \(17.43\).

Thus, the estimated average speed (distance per hour) is approximately \(17.43\) miles per hour.

Final thought: The cyclist rode about \(17.43\) miles in 1 hour. To summarize:

  • We first calculated the average speed from the total distance and total time, dividing roughly \(60.9\) by \(3.5\).
  • We then simplified for easier division resulting in an estimation of approximately \(17.43\) miles per hour.