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Sagot :
Answer:
Part A
The system of equations are;
x = y/18
x + 1/6 = y/13
Part B
13/30 hours
Step-by-step explanation:
The path on which Anita is riding = The path on which Brad is riding
The point at which Anita starts riding = The start of the park
The rate at which Anita is riding = 18 miles per hour
The time at which Bras began = 10 minutes ahead of Anita
The rate at which Brad is riding = 13 miles per hour
Part A
Let 'x' represent the number of hours it takes Anita and Brad to travel 'y' miles along the path, we have;
The 'x' number of hours it takes Anita to travel 'y' miles is given as follows;
x = y/18
For Brad, we have;
10 minutes = 1/6 of an hour
The 'x'' number of hours it takes Brad to travel 'y' miles is given as follows;
x' = y/13
The duration Brad has traveled, when Anita has traveled for 'x'' hours = x + 1/6 hour
x' = x + 1/6
∴ x + 1/6 = y/13
Part B
Therefore, to travel the same 'y' mile as Anita , we have;
x + 1/6 = y/13
y = 13 × (x + 1/6) = 13·x + 13/6
y = 13·x + 13/6
For Anita, we had; x = y/18
∴ y = x × 18 = 18·x
Equating both y-values gives;
y = y
∴ 13·x + 13/6 = 18·x
18·x - 13·x = 5·x = 13/6
x = 13/(5 × 6) = 13/30 hours
The number of hours it will take Anita and Brad to meet on the path = 13/30 hours (equivalent to 13/30 hour × 60 minutes/hour = 26 minutes)
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