# algebra

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Rachel allows herself 1 hour to reach a sale appointment 50 mile s away. After she has driven 30 miles, she realizes that she must increase her speed by 15 miles per hour in order to get there on time. What was her speed for the first 30 miles?

• algebra -

Call the initial speed V (in miles/h) and the time driving at that speed be t (in hours).

V*t + (V+15)*(1-t) = 50

V*t = 30

30 + (V+15)(1 - 30/V) = 50

(V+15)(1 - 30/V) = 20
V + 15 -30 -450/V = 20
V - 450/V = 35
V^2 -35V -450 = 0
(V-45)(V+10) = 0

Only the positive root, V = 45 mph, makes sense. Rachel finishes the trip at 60 mph

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