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500 PS section2 #12

by dunkin77 » Sun Apr 01, 2007 10:40 am
Hi,

My answer was A, but the correct answer is C) (so, obviously my calculation was wrong) Can you help?? Thanks!


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
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by jayhawk2001 » Sun Apr 01, 2007 12:05 pm
The difference in time (1 hr) can be represented by following equation

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

Solving for S, we get 45, -50. Hence C

It might be easier to substitute values from the answer to arrive at
the answer quickly. Choose the middle answer for starters.
We have 450/45 - 450/50 = 1. Which is what we are looking for !
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by dunkin77 » Sun Apr 01, 2007 12:50 pm
Thanks Jay- it's very clear and good idea to try from C). :)
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by BTGmoderatorRO » Sun Oct 15, 2017 7:36 am
The total distance covered during the bus trip is 450 miles.
and, average speed, S, =Total distance covered/ total time taken
S=450/ total time taken
total time taken= 450/S .hour

from the question, the time taken could have been reduced by 1 hour if the average speed S have been increased by 5miles/hr
i.e if Avg. speed (S+5) miles/hr
$$then\ time=\left(\frac{450}{S}d-\frac{1}{ }\right)\ hr$$
$$Therefore,S+5=\frac{total\ dis\tan ce}{\frac{450}{S}-1}$$
Since distance is still the same,
$$Therefore,S+5=\frac{450}{\frac{450}{S}-1}$$
$$\left(S+5\right)\left(\frac{450}{S}-1\right)=450$$
By expanding the expression on the left, we have,
$$450-S+\frac{2250}{S}-5=450$$
$$S+5-\frac{2250}{S}=0$$
$$S^2+5S-2250=0$$
solving this quadratically, we obtain
(S+50)(S-45)=0
S=-50 or S=45 miles/hr

since average speed cannot be negative, we will discard the negative value obtained.
Average speed, S= 45 miles/hr
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by [email protected] » Sun Oct 15, 2017 2:08 pm
Hi All,

While this is an old post, the math concepts in this prompt will be ones that you will see on Test Day. This particular prompt has a built-in shortcut that you can take advantage of. Since the total Distance is 450 miles - and the DIFFERENCE in TIMES is exactly 1 hour, we will almost certainly need two different speeds that BOTH divide evenly into 450... and that DIFFER by 5 miles/hour and would lead to a 1 hour difference in time-traveled. Looking at the answer choices, the only possibility that stands out would be if the speeds were 45 and 50 (since both of those values divide evenly into 450 and differ by 5). If we 'TEST' those speeds against that distance, we find....

450 mi = (45 mi/hour)(10 hours)
450 mi = (50 mi/hour)(9 hours)

This is an exact match for what we were told. We're asked for the slower speed...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Sun Nov 24, 2019 5:21 pm
dunkin77 wrote:Hi,

My answer was A, but the correct answer is C) (so, obviously my calculation was wrong) Can you help?? Thanks!


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

Scott Woodbury-Stewart
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[email protected]

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by Brent@GMATPrepNow » Mon Nov 25, 2019 10:38 am
dunkin77 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
Brent Hanneson - Creator of GMATPrepNow.com
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