Question 95836: Your school is 18 3/4 miles south of Pittsburgh and your house is 44 1/4 miles south of Pittsburgh. You leave your school at 5:00 P.M., traveling south by bicycle at an average speed of 15 miles per hour. Your father leaves Pittsburgh in a car at 5:45 P.M. He is driving south at an average speed of 55 miles per hour. Let t represent the time it takes your father to drive from Pittsburgh toward your house.
1. Find the time it would take you to ride your bicycle home.
2. Find the time your father will arrive home.
3. Write an equation to find your distance d1, from Pittsburgh after t hours.
4. Write an equation to find your father's distance d2 from Pittsburgh after t hours.
5. Use your equations from Exercises 3 and 4 to find how long it takes your father to pass you.
6. Find the number of hours you rode your bicycle when your father passes you.
7. At what time did your father pass you on your bicycle?
8. How many miles did you ride your bicycle when your father passed you?
9. You want to arrive home before your father. Assume that all other information stays the same. What time should you leave school?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Your school is 18 3/4 miles south of Pittsburgh and your house is 44 1/4 miles south of Pittsburgh. You leave your school at 5:00 P.M., traveling south by bicycle at an average speed of 15 miles per hour. Your father leaves Pittsburgh in a car at 5:45 P.M. He is driving south at an average speed of 55 miles per hour. Let t represent the time it takes your father to drive from Pittsburgh toward your house.
1. Find the time it would take you to ride your bicycle home.
t = d/r; t=(44 1/4 - 18 3/4)/15 = 25.5/15 = 1.7 hrs
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2. Find the time your father will arrive home.
t = d/r; t= [44 1/4] /55 =0.804545... hrs
0.804544*60 *60 min = 48.27 minutes
5:45 + 48.27 min = 6:33
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3. Write an equation to find your distance d1, from Pittsburgh after t hours.
d1 =18.75 + 15t
4. Write an equation to find your father's distance d2 from Pittsburgh after t hours.
d2 = 55t
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5. Use your equations from Exercises 3 and 4 to find how long it takes your father to pass you.
Son leaves school 45 minutes before father leaves Pittsburgh.
d1 = 18.75 + 15(t+(3/4))
d2 = 55t
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Father passes son when there distances from Pittsburg are the same:
55t = 18.75+15t+15*(3/4)
40t = 18.75+11.25
40t = 30
t = 3/4 hr or 45 minutes
Father will pass Son after Father has been on the road 45 minutes.
That's at 6:30
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Find the number of hours you rode your bicycle when your father passes you.
45 min + 45 min = 1 1/2 hrs.
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7. At what time did your father pass you on your bicycle?
6:30
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8. How many miles did you ride your bicycle when your father passed you?
(3/2)hr*15 mph = 22 1/2 miles
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9. You want to arrive home before your father. Assume that all other information stays the same. What time should you leave school?
To get there the same time father travels 44.25 miles when son travels
44.25-18.75 mi = 25.5 miles distance son goes; 44.25= distance father goes
Son time from 5:00 = 25.5/15 = 1.7 hrs
Father time = 44.25/55 = 0.804545 hrs from 5:45
Adding the 0.75 hr to the father's time he took 1.5545 hrs from 5:00
Difference is 1.7-1.5545 = 0.1455 hrs or 8.73 minutes
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Son need to leave school more than 8.73 minutes earlier.
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Cheers,
Stan H.
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