Problema Solution
Serena left home at 8:00A.M, determined to make the ten- mile trip to school on bicycle for a change. Soon thereafter, a parent noticed forgotten math homework on kitchen table, got into the family car, and tried to catch up with the forgetful child. Serena had 15 minute head start, and was pedaling at 12 mph, while the parent pursued at 30 mph. Was Serena reunited with the homework before reaching school that day? If so, where? If not, at what time during first period(math which start at 9:00) was the homework delivered?
Answer provided by our tutors
Let
v1 = 12 mph Serena's speed
v2 = 30 mph parent's speed
t = Serena's time
t - 15/60 = t - 1/4 parent's time
d = 10 mi the distance from home to school
We will use the formulas for distance (distance = speed*time) and time (time = distance/speed).
Serena is reunited with the homework before reaching school means the solution of the following equation:
v1*t = v2(t - 1/4) for t is less than d/v1 = 10/12 = 5/6 hr = 5*60/6 = 50 min
12t = 30(t - 1/4)
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click here to see the equation solved for t
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t = 5/12 hr
t = 5*60/12 min
t = 25 min
Since 25 < 50 follows Serena will be reunited with the homework before reaching the school.
v1*t = 12*(5/12) = 5 mi
She will reunited with the homework at a distance of 5 miles from home.