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A train travels at the rate of 10 miles/hr for the first hou

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A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post Updated on: 08 Jun 2013, 04:14
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A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 450-mile journey? Assume that the train makes no intermediate stops.

A. 8
B. 8.5
C. 9
D. 9.5
E. 10

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Originally posted by atalpanditgmat on 08 Jun 2013, 02:51.
Last edited by Bunuel on 08 Jun 2013, 04:14, edited 1 time in total.
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Re: A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 08 Jun 2013, 03:06
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Every hour the train travels 10 miles more than the hour before: \(10,20,30,...\)
When will this sum equal \(450\)?

\(10+20+30+...=450\). We can divide everything by 10 and obtain \(1+2+3+...=45\). To calculate the sum of the first n integers we can use \(\frac{n(n+1)}{2}\).
\(\frac{n(n+1)}{2}=45\), \(n(n+1)=90\) \(n=9\)

C 9
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Re: A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 08 Jun 2013, 04:24
atalpanditgmat wrote:
A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 450-mile journey? Assume that the train makes no intermediate stops.

A. 8
B. 8.5
C. 9
D. 9.5
E. 10


\(time_1*distance_1+time_2*distance_2+time_3*distance_3+...+time_t*distance_t=450\).

Now, \(time_1=time_2=time_3=...=time_t=1\) hour and \(distance_1=10\) miles, \(distance_2=30\) miles, \(distance_3=30\) miles, ..., \(distance_t=t*10\) miles,

So, we have that \(1*(10+20+30+...t*10)=450\) --> \(1+2+3+...t=45\) --> \(\frac{1+t}{2}*t=45\) --> \(t=9\).

Answer: C.

Hope it's clear.
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Re: A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 15 Aug 2013, 11:11
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A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 450-mile journey? Assume that the train makes no intermediate stops.

I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)


Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
7 70 280
8 80 360
9 90 450

It takes a total of nine hours to cover the 450 mile distance.

ANSWER: C. 9
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Re: A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 25 Jan 2014, 12:07
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Also remember that the sum of the first 5 integers is 15 and the sum of the first 10 integers is 55. Therefore, he will need only 9 hours to get to 450.
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A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post Updated on: 19 Jan 2016, 12:57
total miles/hours (h)=5(h+1)
450/h=5(h+1)
h^2+H-90=0
h=9 hours

Originally posted by gracie on 29 Aug 2015, 18:26.
Last edited by gracie on 19 Jan 2016, 12:57, edited 2 times in total.
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Re: A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 19 Jan 2016, 07:06
The total rate of the trip must be a multiple of 10, since the different rates are increasing constantly by 2.
Total Time= Total Distance/Total Rate. Plugging in the total time using the answer choices and resolving for the rate, we get only one time value that generates a rate multiple of 10 and that is T=9. (450/9 =50)
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Re: A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 20 Mar 2017, 04:40
atalpanditgmat wrote:
A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 450-mile journey? Assume that the train makes no intermediate stops.

A. 8
B. 8.5
C. 9
D. 9.5
E. 10


in first hour it travels 10 miles
in second hour it travels 20 miles
like wise adding up
10 +20 +30.........10n = 450
n/2(10 +10n) = 450
or n = 9
therefore it will cover the distance in 9 hrs
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Re: A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 22 Mar 2017, 09:42
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atalpanditgmat wrote:
A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 450-mile journey? Assume that the train makes no intermediate stops.

A. 8
B. 8.5
C. 9
D. 9.5
E. 10


Let us assume the train completes the journey after n hours. Then,

10 + 20 + 30 + … + 10n = 450

Let’s factor 10 from the left hand side:

10(1 + 2 + 3 + … + n) = 450

1 + 2 + 3 + … + n = 45

n(n + 1)/2 = 45

n(n + 1) = 90

n = 9 or n = -10

Since n cannot be negative, then n = 9.

Answer: C
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Re: A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 13 Apr 2018, 07:25
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atalpanditgmat wrote:
A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 450-mile journey? Assume that the train makes no intermediate stops.

A. 8
B. 8.5
C. 9
D. 9.5
E. 10


First check the answer choices (ALWAYS check the answer choice before deciding on an approach to a question)

We see that all answer choices are between 8 hours and 10 hours.
So, let's test the answer choices, starting with 8 hours, and then go from there (if need be).

A) 8 hours
Distance = (rate)(time)
So, the train travels 10 miles in the 1st hour, 20 miles in the 2nd hour, 30 miles in the 3rd hour, . . . . . 80 miles in the 8th hour
So, TOTAL distance traveled = 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 = 360 miles
We want the train to travel 450 miles, so we need to keep going

ASIDE: We know that the train travels 90 miles in the 9th hour.
So, AFTER 9 hours the distance the train has traveled = 360 miles + 90 miles = 450 VOILA!!

Answer: C

Cheers,
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A train travels at the rate of 10 miles/hr for the first hou [#permalink]

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New post 14 Apr 2018, 22:38
atalpanditgmat wrote:
A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 450-mile journey? Assume that the train makes no intermediate stops.

A. 8
B. 8.5
C. 9
D. 9.5
E. 10


Hour - Distance
1st - 10
2nd - 20
3rd - 30
4th - 40
5th - 50
6th - 60
7th - 70
8th - 80
9th - 90

9 hrs = 450 miles

(C)
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A train travels at the rate of 10 miles/hr for the first hou   [#permalink] 14 Apr 2018, 22:38
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