Final answer:
The equation is t = 5m, which represents the proportional relationship where t is the time in minutes and m is the distance in miles.
Step-by-step explanation:
Danny rode his bike at a constant speed, covering a distance of 1 mile in 5 minutes. To represent the proportional relationship between the distance m in miles and the time t in minutes, we can use a simple equation. Since Danny takes 5 minutes to ride 1 mile, the relationship is direct and proportional; for every mile he rides, he will need an additional 5 minutes. Therefore, the equation to describe this proportional relationship is t = 5m.
We can arrive at this equation by first understanding the concept of a proportional relationship. A proportional relationship means that when one quantity increases, the other increases at a constant rate. In this case, the time it takes (t) increases by 5 minutes for every 1 mile (m) increased in distance, which we can write as the ratio of 1 mile / 5 minutes. Consequently, we can set up the equation t / m = 5 / 1, which simplifies the equation t = 5m, representing the time in minutes it takes to travel a certain distance in miles at the given speed.