SOLUTION: if the speed limit is decreased by 10 km/h on a 100 km stretch of a highway, the trip will take a half hour longer than usual. what is the usual speed limit

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Question 1015582: if the speed limit is decreased by 10 km/h on a 100 km stretch of a highway, the trip will take a half hour longer than usual. what is the usual speed limit
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39627)   (Show Source): You can put this solution on YOUR website!
How long does the trip take USUALLY? t.
How long does trip take at the new speed limit? t+1/2. 
Usual           r         t          100
New Limit      r-10      t+1/2       100

RT=D travel rate rule.
Do you know what to do?


(1) Form a system of equations
(2) Solve the system for r and t.
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!
if the speed limit is decreased by 10 km/h on a 100 km stretch of a highway, the trip will take a half hour longer than usual. what is the usual speed limit
Let usual speed limit be S

Then time taken at usual speed = 

Decreasing the speed makes the new speed, S – 10

Time taken at new speed: 

We then get:  

100(2)(S – 10) = 100(2S) – S(S – 10) ------- Multiplying by LCD, 2S(S – 10) 







(S - 50)(S + 40) = 0

S, or original speed limit =  

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