Four Minutes after Monica left to go to school with her mom

Four Minutes after Monica left to go to school with her mom, her Dad realized that she had left her math homework at home. He decided to bring it to her so she would not get in trouble. Since he was driving at a speed 20 mph more than Monica\'s mom, he caught up with her after 8 miles from their house. What was Monica\'s dad\'s speed?

Solution

Four Minutes after Monica left to go to school with her mom, her Dad realized that she had left her math homework at home. He decided to bring it to her so she would not get in trouble. Since he was driving at a speed 20 mph more than Monica\'s mom, he caught up with her after 8 miles from their house. What was Monica\'s dad\'s speed?
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Dad DATA:
distance = 8 miles ; rate = m+20 mph ; time = 8/(m+20) hrs.
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Mom DATA:
distance = 8 miles ; rate = m mph ; time = 8/m hrs.
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Equation:
Mom time - Dad time = 4 minutes = (1/15) hour
8/m - 8/(m+20) = 1/15
8*15*(m+20) - 8*15m = m(m+20)
8*16*20 = m^2 + 20m
m^2 + 20m - 2400 = 0
(m+60)(m-40) = 0
Positive solution: m = 40 mph (Mom\'s speed)
m+20 = 60 mph (Dad\'s speed)