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

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by swerve » Wed Jun 27, 2018 9:38 am

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

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

The OA is C.

Please, can anyone explain this PS question? I tried to solve it but I need help. Thanks.
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by [email protected] » Wed Jun 27, 2018 9:53 am
Hi swerve,

We're told that a train travels from city A to city B, the average speed of the train is 60 m/hr and it travels the first quarter of the distance at a speed of 90 m/hr. We're asked for the speed of the train over the remaining distance. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF....total distance = 360 miles....
the first 1/4 of the trip = 90 miles; at 90 miles/hour, it would take 1 hour

Total Distance = (Av. Speed)(Total Time)
360 miles = (60 miles/hour)(Total T)
360/60 = T
Total time = 6 hours

the remaining 3/4 of the trip = 360 - 90 = 270 miles
the remaining time = 6 - 1 = 5 hours
(270)/(5 hours) = 54 miles/hour for the rest of the trip.

Final Answer: C

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by Jeff@TargetTestPrep » Mon Jul 30, 2018 10:30 am
swerve wrote:A train travels from city A to city B. The average speed of the train is 60 m/hr and it travels the first quarter of the trip at a speed of 90 m/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

Answer: C

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