During a 220 meter relay race, Jack begins at the starting line and runs for 4 minutes and then passes the baton to Jill. She runs for 3 minutes and finishes the race. If Jack can run 20 meters per minute faster than Jill, then what is Jack's rate of speed?
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To find Jack's rate of speed, we need to first determine the distance he ran during his 4 minutes of running.
We are given that the entire race is 220 meters long, and Jill ran for 3 minutes. Since Jack started the race, the total time of the race is 4 + 3 = 7 minutes.
Let's assume Jill's rate of speed is x meters per minute. Since we know that Jack runs 20 meters per minute faster than Jill, his rate of speed will be x + 20 meters per minute.
We can set up an equation to represent the distance each person ran:
Jill's distance = Jill's rate of speed * Jill's time
Jack's distance = Jack's rate of speed * Jack's time
Jill's distance = x * 3
Jack's distance = (x + 20) * 4
We also know that the total distance of the race is equal to the sum of the distances each person ran:
Jill's distance + Jack's distance = 220
Substituting the values we have:
x * 3 + (x + 20) * 4 = 220
Next, we can simplify and solve for x:
3x + 4(x + 20) = 220
3x + 4x + 80 = 220
7x + 80 = 220
7x = 220 - 80
7x = 140
x = 140/7
x = 20
Therefore, Jill's rate of speed is 20 meters per minute.
To find Jack's rate of speed, we add 20 meters per minute to Jill's rate of speed:
Jack's rate of speed = Jill's rate of speed + 20
Jack's rate of speed = 20 + 20
Jack's rate of speed = 40 meters per minute.
So, Jack's rate of speed is 40 meters per minute.