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# A train travels from city A to city B. The average speed of the train

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A train travels from city A to city B. The average speed of the train  [#permalink]

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04 Nov 2014, 00:03
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Difficulty:

55% (hard)

Question Stats:

64% (02:41) correct 36% (02:28) wrong based on 199 sessions

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A train travels from city A to city B. The average speed of the train is 60 miles/hr and it travels the first quarter of the trip at a speed of 90 mi/hr. What is the speed of the train in the remaining trip?

A. 30
B. 45
C. 54
D. 72
E. 90

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Re: A train travels from city A to city B. The average speed of the train  [#permalink]

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10 Nov 2014, 20:00
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Refer diagram below:

Attachment:

speed.png [ 3.39 KiB | Viewed 3540 times ]

Setting up the time equation:

Total time = Time required in first quarter + Time required in the remaining journey

$$\frac{d}{60} = \frac{d}{4*90} + \frac{3d}{4*s}$$

$$s = \frac{90*3}{5} = 54$$

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A train travels from city A to city B. The average speed of the train  [#permalink]

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30 Jan 2015, 06:23
Using the RTD chart, with A being the first quarter, B the rest of the trip and All the combined "trip".

_______R_____T______D
A.........90........3..........270
B.........54.......15.........810
All........60.......18........1080

Let me explain how we fill in the chart:
1) Starting with what we know, we add 90 and 60
2) Picking an easy number for the total distance (6*9=54), so I chose 540. Multiply by 2 to get the whole trip, and we get 1080. Add 1080 for all-distance.
3) 1/4 of the whole distance happened at a Rate of 90. So, 1080/4=270, add 270 under A-D.
4) 2080 - 270 = 810, for the rest of the trip. Add 810 under B-D.
5) Claculate the individual Times for A and All, using T=D/R. Add the results, 3 and 18, under A-T and All-T.
6) 18-3=15, this is the remaining Time for B. Add 15 under B-T.
7) Finally, 15R=810 -->R=810/15 --> R= 54 ANS C
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Re: A train travels from city A to city B. The average speed of the train  [#permalink]

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06 Apr 2017, 09:45
1
1
PareshGmat wrote:
A train travels from city A to city B. The average speed of the train is 60 miles/hr and it travels the first quarter of the trip at a speed of 90 mi/hr. What is the speed of the train in the remaining trip?

A. 30
B. 45
C. 54
D. 72
E. 90

We have an average rate problem in which we can use the following formula:

Avg speed = (distance 1 + distance 2)/(time 1 + time 2)

If we let d = total distance of the trip, then the first quarter of the trip, or (1/4)d = d/4, was traveled at 90 mph. Thus, the time was (d/4)/90 = d/360.

We can let the rate for the remaining part of the trip = r, and thus the time for the remaining part of the trip, or (3/4)d = 3d/4, is (3d/4)/r = 3d/(4r). Let’s use all of this information in the average rate equation:

60 = d/(d/360 + 3d/(4r))

60 = 1/(1/360 + 3/(4r))

60(1/360 + 3/(4r)) = 1

1/6 + 45/r = 1

Let’s multiply the above equation by 6r:

r + 270 = 6r

270 = 5r

r = 54

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Re: A train travels from city A to city B. The average speed of the train  [#permalink]

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08 Apr 2017, 18:53
2
Hi All,

This question can be solved by TESTing VALUES.

The prompt tells us that average speed of the train over the course of the entire trip is 60 miles/hr and that it travels the first quarter of the distance at a speed of 90 mi/hr. We're asked for the average speed of the train for the remaining three-quarters of the trip.

Let's choose 90 miles for the FIRST QUARTER of the distance. We can then immediately calculate two things...
1) Since the train was traveling 90 miles/hour, the first quarter of the trip took 1 hour to complete.
2) Since (1/4)(Total Distance) = 90 miles, then the FULL TRIP = 4(90) = 360 miles.

The total trip is 360 miles; with an average speed of 60 miles/hr, the FULL TRIP would take... (X)(60 mph) = 360 miles.... X = 6 hours to complete.

The first hour of the trip covered 90 miles, so the remaining 360 - 90 = 270 miles of the trip are covered in the remaining 5 hours...

Thus, the average speed for the remainder of the trip is... (270 miles)/(5 hours) = 54 miles/hour

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Re: A train travels from city A to city B. The average speed of the train  [#permalink]

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29 Jul 2018, 07:25
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Re: A train travels from city A to city B. The average speed of the train &nbs [#permalink] 29 Jul 2018, 07:25
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