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John traveled the entire 60 miles trip. If he did the...

This topic has 4 expert replies and 3 member replies

John traveled the entire 60 miles trip. If he did the...

Post Sat Jan 13, 2018 1:28 pm
John traveled the entire 60 miles tirp. if he did the first 12 miles of a constant rate 24 miles per hour and the remaining trip of a constant rate 48 miles per hour, what is the his average speed, in miles per hour?

A. 20 mph
B. 24 mph
C. 30 mph
D. 32 mph
E. 40 mph

The OA is E.

Is there a strategic approach to this PS question? Can any experts help, please?

I know that average speed will be, total distance / total time, but i don't know how can I do or how can I solve this question. I need your help. Thanks!

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DavidG@VeritasPrep Legendary Member
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Post Sun Jan 14, 2018 11:46 am
AAPL wrote:
John traveled the entire 60 miles tirp. if he did the first 12 miles of a constant rate 24 miles per hour and the remaining trip of a constant rate 48 miles per hour, what is the his average speed, in miles per hour?

A. 20 mph
B. 24 mph
C. 30 mph
D. 32 mph
E. 40 mph

The OA is E.

Is there a strategic approach to this PS question? Can any experts help, please?

I know that average speed will be, total distance / total time, but i don't know how can I do or how can I solve this question. I need your help. Thanks!
Well, you could do the math.

First part of trip: it'll take 1/2 hour to go 12 miles at 24 mph.
Second part of trip: There are 60-12 = 48miles remaining. It'll take 1 hour to cover those 48 miles at 48mph.

Total distance:60
Total time: 1/2 + 1 = 1/5 hours
Avg rate: 60/1.5 = 40 mph. The answer is E

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Post Sun Jan 14, 2018 11:48 am
AAPL wrote:
John traveled the entire 60 miles tirp. if he did the first 12 miles of a constant rate 24 miles per hour and the remaining trip of a constant rate 48 miles per hour, what is the his average speed, in miles per hour?

A. 20 mph
B. 24 mph
C. 30 mph
D. 32 mph
E. 40 mph

The OA is E.

Is there a strategic approach to this PS question? Can any experts help, please?

I know that average speed will be, total distance / total time, but i don't know how can I do or how can I solve this question. I need your help. Thanks!
But you can see that if John spent the same amount of time traveling at 24mph and at 48mph, he'd have traveled at (24 + 48)/2 = 72/2 = 36 mph. So long as you see that he spent more time traveling at 48mph than at 24 mph, we know his average would have been pulled towards the faster speed, and thus that average would to be greater than 36 mph. Only E works.

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DrMaths Senior | Next Rank: 100 Posts Default Avatar
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Post Mon Jan 15, 2018 4:51 am
Using speed = distance/time, we get time = speed over distance,
so total time, T = t1 + t2 = 12/24 + 48/48 = 1.5

Average speed = D/T = 60/1.5 = 40

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Imthatguy Newbie | Next Rank: 10 Posts Default Avatar
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Post Mon Jan 15, 2018 5:34 am
AAPL wrote:
John traveled the entire 60 miles tirp. if he did the first 12 miles of a constant rate 24 miles per hour and the remaining trip of a constant rate 48 miles per hour, what is the his average speed, in miles per hour?

A. 20 mph
B. 24 mph
C. 30 mph
D. 32 mph
E. 40 mph

The OA is E.

Is there a strategic approach to this PS question? Can any experts help, please?

I know that average speed will be, total distance / total time, but i don't know how can I do or how can I solve this question. I need your help. Thanks!
12 miles at 24 mph = 30 mins.
48 miles at 48 mph = 60 mins.

Total time taken = 30+60 = 90 mins.
Total distance = 60 miles.

Average speed = (60/90) * 60 = 40 mph.

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Post Mon Jan 15, 2018 11:34 am
Hi AAPL,

We're told that John tool a 60 miles trip; the first 12 miles of a constant rate 24 miles per hour and the remaining distance at a constant rate 48 miles per hour. We're asked for the average speed, in miles per hour, for the entire trip. To answer this question, you might find it easiest to break the calculation down into 'pieces.'

1st part of the trip: 12 miles at 24 miles/hour....
Distance = (Rate)(Time)
12 miles = (24 mi/hour)(T)
12/24 = T
T = 1/2 hour

2nd part of the trip: 48 miles at 48 miles/hour....
Distance = (Rate)(Time)
48 miles = (48 mi/hour)(T)
48/48 = T
T = 1 hour

Total Distance = 60 miles
Total Time = 1.5 hours

Total Distance = (Av. Speed)(Total Time)
60 miles = (X)(1.5 hours)
60/1.5 = X
120/3 = X
X = 40 miles per hour

Final Answer: E

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Rich

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Post Thu Jan 18, 2018 1:36 pm
AAPL wrote:
John traveled the entire 60 miles tirp. if he did the first 12 miles of a constant rate 24 miles per hour and the remaining trip of a constant rate 48 miles per hour, what is the his average speed, in miles per hour?

A. 20 mph
B. 24 mph
C. 30 mph
D. 32 mph
E. 40 mph
We can use the formula:

Average speed = (total distance/total time)

The time for the first 12 miles was 12/24 = 0.5 hour.

The time for the remaining 48 miles was 48/48 = 1 hour.

Thus:

Average speed = 60/1.5 = 40 mph

Answer: E

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elias.latour.apex Master | Next Rank: 500 Posts
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Post Thu Jan 18, 2018 6:12 pm
If you're doing a lot of math, chances are you're doing something wrong. The Quant part of the GMAT isn't a math test -- it's a test of reasoning ability.

If you travel half of the trip at 24 mph and the other half at 48 mph, then you will average 36 mph. However, John only did 12 miles of 60 miles at the slow speed. Granted, it's about the TIME spent not the DISTANCE, but even so, it's obvious that the answer must be greater than 36 mph. There is only one choice that is greater than 36 mph, and that's (E). Next problem!

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