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A trip of 900 miles would have taken 1 hour less if the average speed

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A trip of 900 miles would have taken 1 hour less if the average speed [#permalink] New post   29 Oct 2023, 23:12
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A trip of 900 miles would have taken 1 hour less if the average speed for the trip had been greater by 10 miles per hour. What was the average speed for the trip?

(A) 40 miles per hour
(B) 45 miles per hour
(C) 60 miles per hour
(D) 75 miles per hour
(E) 90 miles per hour


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A trip of 900 miles would have taken 1 hour less if the average speed [#permalink] New post   02 Dec 2023, 09:41
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We can interpret into this equation, where r = average speed for the trip.
\(\frac{900}{r }- 1 =\frac{ 900}{r+10}\)
= \(\frac{900-r}{r}\)

Cross-multiply to set up:
\(900-r(r+10) = 900r\)
\(900r+9000-r^2-10r = 900r\)
\(r^2+10r-9000=0\)
\((r+100)(r-90)=0\)

Since r can't be a negative value, the answer is 90.
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gmatclubot
A trip of 900 miles would have taken 1 hour less if the average speed [#permalink]
02 Dec 2023, 09:41
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