Problem Solving

Hi All,

We're told that 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. We're asked for the average speed S, in miles per hour, for the trip. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, it's worth noting that increasing the speed by 5 miles/hour would decrease the travel time by EXACTLY 1 HOUR. This implies that the original speed and the increased speed are both factors of 450 (which is why the decrease in time is a nice 'round' number: 1 hour). Thus, we should look to TEST the answers that are divisors of 450. Let's TEST Answer D first...

Answer D: 50 miles/hour
At 50 miles/hour, the trip would take 450/50 = 9 hours
At 55 miles/hour, the trip would take 450/55 = something between 8 hours and 9 hours. This would NOT lead to a difference of 1 hour (and notice how 55 is NOT a divisor of 450). However, 45 IS a divisor.... so let's TEST answer C next...

Answer C: 45 miles/hour
At 45 miles/hour, the trip would take 450/45 = 10 hours
At 50 miles/hour, the trip would take 450/50 = 9 hours
This is an exact different of 1 hour, so this must be the answer.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC 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

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/speed
So, 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

BTGmoderatorDC 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

Let t = the time to complete the trip of 450 miles when the average speed is S. Thus, we have:

St = 450

and

(S + 5)(t - 1) = 450

Isolating t in the first equation, we have: t = 450/S. Substituting this in the second equation, we have:

(S + 5)(450/S - 1) = 450

450 - S + 2250/S - 5 = 450

-S + 2250/S - 5 = 0

S + 5 - 2250/S = 0

S^2 + 5S - 2250 = 0

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

S = -50 or S = 45

Since S can't be negative, S = 45.

Answer: C