Ito is training to run a 10 kilometer race in five months. His current pace is 6.25 minutes per kilometer. He wants to constantly increase his speed each month until he is running a 5.5 minute kilometer.
Ito needs to increase his pace by ____ each month.
Complete the equation to represent Ito's speed where x is the number of the training month and y is his speed in kilometers per hour. y = ___ x + ____
(6.25-5.50)/5 = 0.15 min/km/mo
now use that to form the equation.
To find the amount by which Ito needs to increase his pace each month, we can calculate the difference between his current pace and his target pace.
The difference between Ito's current pace of 6.25 minutes per kilometer and his target pace of 5.5 minutes per kilometer is:
6.25 minutes/km - 5.5 minutes/km = 0.75 minutes/km
Now, we need to convert this difference of 0.75 minutes per kilometer to seconds per kilometer, since the equation uses minutes and seconds.
0.75 minutes/km * 60 seconds/minute = 45 seconds/km
So, Ito needs to increase his pace by 45 seconds per kilometer each month.
Now, let's represent Ito's speed with an equation, where x is the number of the training month and y is his speed in kilometers per hour.
The units of the pace are minutes per kilometer, but we need to convert it to kilometers per hour to match the units on the y-axis.
The equation for Ito's speed can be represented as:
y = (60 / (6.25 - (0.75 * x)))
Here, the 60 is the conversion from minutes to hours, 6.25 is the initial pace in minutes per kilometer, and (0.75 * x) is the increase in pace for each training month.