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A train travels at the rate of 10 miles/hr for the first hour of a tri
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21 Jun 2022, 01:38
21 Jun 2022, 01:38
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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
A. 8
B. 8.5
C. 9
D. 9.5
E. 10
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Re: A train travels at the rate of 10 miles/hr for the first hour of a tri
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21 Jun 2022, 06:05
21 Jun 2022, 06:05
1
Carcass 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
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
Re: A train travels at the rate of 10 miles/hr for the first hour of a tri
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23 Feb 2023, 14:22
23 Feb 2023, 14:22
I used the following formula:
the sum of first n integers= (n (n+1))/2
We need the sum of 10+20+30+... The sum equals 450, so
n (n+10) = 900. We can solve the quadratic or test choices. Choice C fits.
the sum of first n integers= (n (n+1))/2
We need the sum of 10+20+30+... The sum equals 450, so
n (n+10) = 900. We can solve the quadratic or test choices. Choice C fits.
