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A train travels at the rate of 10 miles/hr for the first hou
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Updated on: 08 Jun 2013, 03:14
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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 450mile 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
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08 Jun 2013, 02:06
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
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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 450mile 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
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15 Aug 2013, 10:11
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 450mile 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
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25 Jan 2014, 11:07
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
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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+H90=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
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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
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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 450mile 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
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22 Mar 2017, 08:42
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 450mile 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
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13 Apr 2018, 06:25
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 450mile 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 milesWe 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, Brent
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A train travels at the rate of 10 miles/hr for the first hou
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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 450mile 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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