Question

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 + ____

Answer 1

\[original ~speed~u=\frac{ 1 }{ 6.25 }=\frac{ 100 }{ 625 }km/ \min\]
final speed \[v=\frac{ 1 }{ 5.5 }=\frac{ 100 }{ 550 }~km/\min\]
t=5
let acceleration =a
\[v=u+at\]
\[\frac{ 100 }{ 550 }=\frac{ 100 }{ 625 }+5a,\]
\[5a=\frac{ 100 }{ 550 }-\frac{ 100 }{ 625 }=100\left( \frac{ 1 }{ 550 }-\frac{ 1 }{ 625 } \right)\]
\[5a=100\left( \frac{ 625-550 }{ 550 \times 625 } \right)=100 \times \frac{ 75 }{ 550 \times 625 }\]\[a=\frac{ 6 }{ 275 \times 5 }=\frac{ 6 }{ 1375 }\]
\[y=\frac{ 100 }{ 625 }+\frac{ 6 }{ 1375 }x\]