SOLUTION: From a common position, two cars traveled in opposite directions. One car traveled 2 km faster than the other car. Find the average speed of each car if they are 60 km apart after

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Question 1015447: From a common position, two cars traveled in opposite directions. One car traveled 2 km faster than the other car. Find the average speed of each car if they are 60 km apart after 3 hours.

Answer by macston(5194) (Show Source):
You can put this solution on YOUR website!
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Assuming you mean the second car traveled two kilometers per hour faster:
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60 km / 3 hrs=20 km/hr
The cars are separating at 20 kilometers per hour.
This means their combined speeds are 20 km/hr.
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F = speed of first car; S = speed of second car = F + 2 km/hr
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F + S = 20 km/hr . Substitute (F + 2 km/hr) for S.
F + (F + 2 km/hr) = 20 km/hr
2F + 2 km/hr = 20 km/hr . Subtract 2 km/hr from each side.
2F=18 km/hr . Divide each side by 2.
F = 9km/hr
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ANSWER 1: Average speed of the first car is 9 km/hr.
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S = F + 2 km/hr = 9km/hr + 2km/hr = 11 km/hr
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ANSWER 2: Average speed of the second car is 11 km/hr.
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CHECK:
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(3 hrs)(F) + (3 hrs)(S) = 60 km
(3 hrs)(9 km/hr) + (3 hrs)(11 km/hr) = 60 km/hr
27km + 33 km = 60 km
60 km = 60 km
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If you meant the second car traveled two kilometers further, not faster:
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2 km/3hrs=2/3 km/hr
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F = speed of first car; S = speed of second car = F + 2/3 km/hr
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F + S = 20 km/hr . Substitute (F + 2/3 km/hr) for S.
F + (F + 2/3 km/hr) = 20 km/hr
2F + 2/3 km/hr = 20 km/hr . Subtract 2/3 km/hr from each side.
2F=19 1/3 km/hr . Divide each side by 2.
F = 9 5/6 km/hr
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ANSWER 1: Average speed of the first car is 9 5/6 km/hr.
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S = F + 2/3 km/hr = 9 5/6 km/hr + 2/3 km/hr = 10 1/2 km/hr
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ANSWER 2: Average speed of the second car is 10 1/2 km/hr.
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CHECK:
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(3 hrs)(F) + (3 hrs)(S) = 60 km
(3 hrs)(9 5/6 km/hr) + (3 hrs)(10 1/2 km/hr) = 60 km/hr
27 15/6 km + 30 3/2 km = 60 km
28 1/2 km + 31 1/2 km = 60 km
60 km = 60 km
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