SOLUTION: 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 th

Question 937638: 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.
B) write and solve an equation that represents the difference in their average speeds

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
---
Matteo DATA:
dist = 400 km ; time = x-1 hrs ; rate = 400/(x-1) kph
-----------------------------------
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
------
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::
-------------
x = 5 hrs (time for Amber)
x-1 = 4 hrs (time for Matteo)
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Cheers,
Stan H.
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