Bunuel wrote:

A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?

(A) 10

(B) 40

(C) 45

(D) 50

(E) 55

Kudos for a correct solution.

Let's start with a

word equation:

travel time at actual speed =

travel time at faster speed + 1 hour

In other words:

travel time at S mph =

travel time at (S + 5) mph + 1 hour

travel time = distance/speedSo, we get:

450/S=

450/(S + 5) + 1

Multiply both sides by S to get: 450 = 450S/(S+5) + S

Multiply both sides by S+5 to get: 450(S + 5) = 450S + S(S+5)

Expand: 450S + 2250 = 450S + S² + 5S

Subtract 450S from both sides: 2250 = S² + 5S

Rewrite as: S² + 5S - 2250 = 0

Factor: (S + 50)(S - 45) = 0

So, EITHER S = 50, OR S = 45

Since the speed can't be negative, the correct answer must be S = 45

Answer: C

Cheers,

Brent

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