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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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Updated on: 08 Jun 2013, 03:14
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Question Stats:

82% (01:46) correct 18% (02:04) wrong based on 265 sessions

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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, 01:51.
Last edited by Bunuel on 08 Jun 2013, 03:14, edited 1 time in total.
Edited the question.
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Re: A train travels at the rate of 10 miles/hr for the first hou  [#permalink]

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08 Jun 2013, 02:06
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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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08 Jun 2013, 03:24
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 $$1*(10+20+30+...t*10)=450$$ --> $$1+2+3+...t=45$$ --> $$\frac{1+t}{2}*t=45$$ --> $$t=9$$.

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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15 Aug 2013, 10:11
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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.

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

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25 Jan 2014, 11:07
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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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Updated on: 19 Jan 2016, 11:57
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, 17:26.
Last edited by gracie on 19 Jan 2016, 11:57, 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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19 Jan 2016, 06:06
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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20 Mar 2017, 03:40
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
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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22 Mar 2017, 08:42
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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.

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

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13 Apr 2018, 06:25
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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!!

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

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14 Apr 2018, 21:38
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 &nbs [#permalink] 14 Apr 2018, 21:38
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