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

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

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New post 27 Oct 2017, 14:11
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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
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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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New post 29 Oct 2017, 18:06
=>

90 / (18/36 + 72/72) = 90 / 1.5 = 60

Therefore, the answer is E.
Answer: E
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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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New post 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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New post 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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New post 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

Answer: E
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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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New post 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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