GMAT Prep Test: Susan Drove an Average Speed...

[Guest]

Susan drove an average speed of 30 mph for the first 30 minutes of a trip. She did drove 60 mph for the next 30 minutes. If she made no stops, what was the average speed, in miles per hour, for the entire trip?

a. 35
b. 40
c. 45
d. 50
e. 55

I get answer C. The correct answer is listed as B.

30mph x 0.5 hours = 15 miles; 60mph x 0.5 hours = 30 miles
Total distance = 45 miles
Total time = 1 hour

Therefore average speed for the entire trip = 45 mph.

Can't figure out how to get 40.

[RonPurewal]

your workup is entirely correct, leading me to believe that perhaps you misread the problem.

are you sure it didn't say this (changes in bold):
"Susan drove an average speed of 30 mph for the first 30 miles of a trip. She did drove 60 mph for the next 30 miles"
?

in this case:
time for first leg of trip = 30 miles / (30 mi/hr) = 1 hr
time for second leg of trip = 30 miles / (60 mi/hr) = 0.5 hr
total time = 1.5 hr

average speed = 60 mi / 1.5 hr = 40 mi/hr

if the problem really says what you've posted, though, then you're correct.

[Guest]

It's definitely "MILES" :)

[FA]

Hi Ron,
Is there a possibility of solving Distance Speed Questions with 2 same distances but different speeds and times by using the weighted averages concept?
Kind Regards,
FA

[Sage Pearce-Higgins]

I would advise you against using weighted averages for speed-distance problems. The big trap comes here from confusing different times with different distances (as the other student did above). After all, 30 miles at 30mph followed by 30 miles at 60mph doesn't mean the average speed was 45mph. This is because Susan spend longer travelling at 30mph. I guess you could use the weighted average principle to think "she spends twice as long travelling at 30mph than at 60mph", but it's more confusing (for me, anyway).

It's much safer to remember that speed = total distance / total time, and work out the totals before plugging them in rather than hoping for a shortcut. Try out question 24 from the diagnostic test in OG 2017. This is a tricky question, be warned!