Answer:
I'll assume "position 7" refers to distance and not to the order of other people.
Explanation:
We want an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0). We can assume that "claps" is a new measure of distance. 0 claps is the finish.
Let's express the information provided in point format.
"At 2 claps, Joe is in position 7" is (2,7) 2 is the distance (claps) and 7 is the time (minutes)
And we can say the rate is also the slope of a line. "rate of 3 claps per minute" is 3c/m, where c is claps and m is minutes.
We can start a line equation by stating y = 3x + b, where we're using the rate, 3 c/m, as the slope, m.
We need to determine the value of b. We can use the given point (2,7) and solve for m:
y = 3x + b
7 = 3*(2) + b
b = 1
The equation becomes y = 3x + 1
y is the distance in claps and x is the time in minutes.
At a time of 2 claps he is at position of 7. b = 1 means he started 1 clap further from the finish at 0 claps.
To find the time required to reach the finish, we need to know the total distance, in claps.