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.
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Per the question,

\(\frac{450}{s}\) - \(\frac{450}{s+5}\) = 1

Instead of solving, use the options.

Choose s= 45 and see if the statement is satisfied and it does. So C is the correct answer.

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

if S*T=450 miles, then either S or T is a multiple of 9
45 is the only multiple of 9 given as choice for S
450/45mph=10 hours=T
checking: (45+5)(10-1)=50*9=450 miles
45 fits
C.

Hi All,

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:

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Rich
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