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

Question

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

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

Zarrolou · Accepted Answer

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

Bunuel · Answer

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.
.

WholeLottaLove · Answer

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

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

jlgdr · Answer

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.

gracie · Answer

total miles/hours (h)=5(h+1)
450/h=5(h+1)
h^2+H-90=0
h=9 hours

Nadiuska · Answer

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)

KrishnakumarKA1 · Answer

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

JeffTargetTestPrep · Answer

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

BrentGMATPrepNow · Answer

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,
Brent

AkshdeepS · Answer

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)

AyushCrackVerbal · Answer

Formula:

1) Speed =  \frac{Distance}{Time}

Distance = Speed*Time

2) Sum of first n natural numbers =  \frac{n(n+1)}{2}

Let the hours taken by train to complete a 450-mile journey be "n"

Distance covered by train in the 1st hour = 10*1 = 10 miles

Distance covered by train in the 2nd hour = 20*1 = 20 miles

Distance covered by train in the nth hour = 10n*1 = 10n miles

Total distance covered by train in n hours =  10 + 20 + 30 + ...... 10n = 450

10 ( 1 + 2 + ..... n) = 450

10  \frac{(n)(n+1)}{2}  = 450

n(n+1) = 90

n^2 + n - 90 = 0

n^2 + 10n - 9n - 90 = 0

n(n+10) - 9(n+10) = 0

(n-9)(n+10) = 0

n = 9 OR -10

Since n is the number of hours, it cannot be negative. Therefore n = 9 hours

The correct answer is  C

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