SOLUTION: distance between point A & point B = 310 KM . two person leave these points at the same time , one with speed of 106km/h and the other with 87km/h . How long does it take to meet e

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Question 165303: distance between point A & point B = 310 KM . two person leave these points at the same time , one with speed of 106km/h and the other with 87km/h . How long does it take to meet each other ?
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
AB = 310 km.
AC = x
BC = 310-x
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T = time
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person leaving from point A is traveling at 87km/h.
person leaving from point B is traveling at 106km/h.
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they both meet at point C.
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person leaving from point A travels x kilometers in T hours.
person leaving from point B travels (310-x) kilometers in T hours.
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rate * time = distance
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person leaving from A equation:
87*T = x
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person leaving from B equation:
106*T = 315-x
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solve both equations for T
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T = x/87 (first equation)
T = (315-x)/106 (second equation)
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since they both equal T then they both equal each other.
x/87 = (315-x)/106
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multiply both sides by (87*106)
equation becomes
106*x = (315-x)*87
remove parentheses.
106*x = 315*87 - 87*x
add 87*x to both sides.
106*x + 87*x = 315*87
perform operations shown.
193*x = 27405
divide both sides by 193.
x = 141.9948187
solve for T in first equation.
x/87 = T
141.9948187/87 = T
T = 1.632124352
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315-x = 173.0051813
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calculate T from second equation.
T = (315-x)/106
T = 173.0051813/106
T = 1.632124352
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point C is 141.9948187 miles from A
point C is 173.0051813 miles from B
AC + BC = 315.
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rate of travel equals distance over time.
141.9948187 / 1.632124352 = 87 km/h
173.0051813 / 1.632124352 = 106 km/h
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answer is T = 1.632124352 hours
They will meet at point C in 1.632124352 hours