<PRE><B>Question 937638</B>
Amber and Matteo are travelling separately from their home Calgary to a wedding 400km away. Amber leaves 1h earlier than matteo, but matteo drives at and average 20km/h faster than amber. If they arrive at the wedding at the exact same time what was their average speed at which each of them traveled?
 a)let x represent the time it takes amber to travel to the wedding, write an expression for the average speed that each person travels.
Amber DATA:
dist = 400 km ; time = x hrs ; rate = 400/x kph
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Matteo DATA:
dist = 400 km ; time = x-1 hrs ; rate = 400/(x-1) kph
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 B) write and solve an equation that represents the difference in their average speeds
Mrate - Arate = 20 kph
400/(x-1) - 400/x = 20 kph
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400x - 400(x-1) = 20x(x-1)
400 = 20x(x-1)
20 = x(x-1)
x^2-x-20 = 0
Factor:
(x-5)(x+4) = 0
Positive solution::
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x = 5 hrs (time for Amber)
x-1 = 4 hrs (time for Matteo)
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Cheers,
Stan H.
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