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Tom traveled the entire 90 km trip. If he travelled the first 18 km of

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Tom traveled the entire 90 km trip. If he travelled the first 18 km of  [#permalink]

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27 Oct 2017, 01:32
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[GMAT math practice question]

Tom traveled the entire 90 km trip. If he travelled the first 18 km of the trip at a constant rate of 36 km per hour and the remaining trip at a constant rate of 72 km per hour, what is his average speed?

A. 30 km/h
B. 36 km/h
C. 45 km/h
D. 48 km/h
E. 60 km/h

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3185 Location: India GPA: 3.12 Tom traveled the entire 90 km trip. If he travelled the first 18 km of [#permalink] Show Tags 27 Oct 2017, 02:01 MathRevolution wrote: [GMAT math practice question] Tom traveled the entire 90 km trip. If he travelled the first 18 km of the trip at a constant rate of 36 km per hour and the remaining trip at a constant rate of 72 km per hour, what is his average speed? A. 30 km/h B. 36 km/h C. 45 km/h D. 48 km/h E. 60 km/h The formula for average speed is $$\frac{(p+q)(ab)}{(qa + pb)}$$ where distance is in the ratio p:q speed of travel in first leg is a, speed in second leg is b. From this question, we get the ratio of the distance to be 1:4(p:q) because he travels the first 18 kms at 36 km/hr and next 72 kms at 72 km/hr Substituting values, the average speed = $$\frac{(1+4)(36*72)}{(72*1 + 36*4)}$$ = $$\frac{5*36*72}{72(1+2)}$$ = 5*12 = 60(Option E) _________________ You've got what it takes, but it will take everything you've got Senior SC Moderator Joined: 22 May 2016 Posts: 2033 Tom traveled the entire 90 km trip. If he travelled the first 18 km of [#permalink] Show Tags 27 Oct 2017, 14:11 1 MathRevolution wrote: [GMAT math practice question] Tom traveled the entire 90 km trip. If he travelled the first 18 km of the trip at a constant rate of 36 km per hour and the remaining trip at a constant rate of 72 km per hour, what is his average speed? A. 30 km/h B. 36 km/h C. 45 km/h D. 48 km/h E. 60 km/h Average speed = $$\frac{TotalDistance}{TotalTime}$$ We need to find the time for each part of the trip (which requires easily finding distance for second part), add the times, and divide into total distance of 90. 1) TIME for Part 1 of trip? RT=D: He traveled 18 km at 36 km per hour. Distance/rate = time, so he took $$Time=\frac{D}{R}: \frac{18}{36}=\frac{1}{2}hr$$ 2) DISTANCE for Part 2? 90 km total, 18 km covered, means (90 - 18) = 72 km remain 3) TIME, Part 2? He traveled 72 km at a speed of 72 km per hour, so $$Time=\frac{D}{R}: \frac{72}{72}= 1 hr$$ 4) AVERAGE SPEED? Total distance = 90 km Total time: $$(\frac{1}{2} + 1)hrs = \frac{3}{2} hrs$$ Average speed in km per hr: $$\frac{90}{(\frac{3}{2})}=(90 * \frac{2}{3})=60$$ Answer E _________________ The only thing more dangerous than ignorance is arrogance. -- Albert Einstein Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6385 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Tom traveled the entire 90 km trip. If he travelled the first 18 km of [#permalink] Show Tags 29 Oct 2017, 18:06 => 90 / (18/36 + 72/72) = 90 / 1.5 = 60 Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: Tom traveled the entire 90 km trip. If he travelled the first 18 km of  [#permalink]

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29 Oct 2017, 19:38
Avg speed = Total distance / total time = 90kms /( 0.5 hrs + 1 hr) = 60 kmph

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Re: Tom traveled the entire 90 km trip. If he travelled the first 18 km of  [#permalink]

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30 Oct 2017, 08:12
MathRevolution wrote:
[GMAT math practice question]

Tom traveled the entire 90 km trip. If he travelled the first 18 km of the trip at a constant rate of 36 km per hour and the remaining trip at a constant rate of 72 km per hour, what is his average speed?

A. 30 km/h
B. 36 km/h
C. 45 km/h
D. 48 km/h
E. 60 km/h

Distance covered in first half = 18 km , Speed = 36km/hr , Time = $$\frac{1}{2} Hr$$
Distance covered in second half = 72 km , Speed = 72 km/hr , Time = 1 Hr

Total time taken = $$\frac{3}{2} Hr$$

So, Average speed = $$\frac{90*2}{3}$$ = $$60 km/hr$$
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Re: Tom traveled the entire 90 km trip. If he travelled the first 18 km of  [#permalink]

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30 Oct 2017, 14:09
MathRevolution wrote:
[GMAT math practice question]

Tom traveled the entire 90 km trip. If he travelled the first 18 km of the trip at a constant rate of 36 km per hour and the remaining trip at a constant rate of 72 km per hour, what is his average speed?

A. 30 km/h
B. 36 km/h
C. 45 km/h
D. 48 km/h
E. 60 km/h

We can let the time for the first 18 km = 18/36 = 1/2 and the time for the rest of the trip = 72/72 = 1; thus:

average speed = (total distance)/(total time)

average speed = 90/(1/2 + 2) = 90/(3/2) = 60 km/h

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Re: Tom traveled the entire 90 km trip. If he travelled the first 18 km of  [#permalink]

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05 Nov 2017, 22:00
average speed = (total distance)/(total time)

72/72 = 1hour
18/36 = 1/2 hour
total km = 90
total time = 1.5 hour
so 90/1.5 = 60 km/hr
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Re: Tom traveled the entire 90 km trip. If he travelled the first 18 km of &nbs [#permalink] 05 Nov 2017, 22:00
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