Final answer:
The time 't' it takes Kiran to bike 10 miles is calculated by dividing the distance by his biking rate 'r', resulting in the equation t = 10 miles / r mph.
Step-by-step explanation:
Kiran plans to bike 10 miles, and we want to write an equation that gives his time t, in hours, as a function of his rate r, in miles per hour. To derive this equation, we use the basic relationship that time is equal to distance divided by rate. The distance Kiran plans to travel is 10 miles.
To represent this relationship as an equation, we divide the distance (10 miles) by the rate (r miles per hour):
t = distance / rate
t = 10 miles / r mph
This equation shows that the time t it takes Kiran to bike 10 miles is a function of the rate r at which he bikes.