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A bicyclist begins a race at a constant rate of 10 miles per hour

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energetics
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A bicyclist begins a race at a constant rate of 10 miles per hour [#permalink] New post   09 May 2019, 16:04
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A bicyclist begins a race at a constant rate of 10 miles per hour, slowing down by 1 mile per hour every half-hour. How many miles has the bicyclist traveled after exactly 2.5 hours?

A) 22.5
B) 20
C) 19
D) 17
E) 12.5
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B
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Re: A bicyclist begins a race at a constant rate of 10 miles per hour [#permalink] New post   09 May 2019, 18:36
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energetics wrote:
A bicyclist begins a race at a constant rate of 10 miles per hour, slowing down by 1 mile per hour every half-hour. How many miles has the bicyclist traveled after exactly 2.5 hours?

A) 22.5
B) 20
C) 19
D) 17
E) 12.5


There are 5 intervals with each 0.5 hrs and the speed of the bicyclist is in decreasing order at the 5 interval points.

We know, Distance=Speed*time
Here , total distance traveled=sum of the distances at 5 intervals=0.5*(10+9+8+7+6)=0.5*40=20 miles.

Ans. (B)
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Re: A bicyclist begins a race at a constant rate of 10 miles per hour [#permalink] New post   02 Sep 2020, 01:34
energetics wrote:
A bicyclist begins a race at a constant rate of 10 miles per hour, slowing down by 1 mile per hour every half-hour. How many miles has the bicyclist traveled after exactly 2.5 hours?

A) 22.5
B) 20
C) 19
D) 17
E) 12.5

total 30 mins interval would be 5

first 30 mins distance would be 5 miles speed 10 mph
2nd interval speed is 9 mph ; 4.5
3rd interval speed 8 mph ; 4
4th interval speed 7mph ; 3.5
5th interval speed 6mph ;3
total distance ; 20 miles
option B
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Re: A bicyclist begins a race at a constant rate of 10 miles per hour [#permalink] New post   02 Sep 2020, 04:56
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The distances traveled every 1/2 hour is an arithmetic progression, with d = -0.5 (as distance keeps reducing)

In the 1st 1/2 hour at 10miles/hour, distance traveled = 5

\(S_n = \frac{n}{2}[2a + (n-1) * d]\)


Here a = 5, n = 5 (2.5 hours is 5 intervals of 1/2 hour each) and d = -0.5

\(S_n = \frac{5}{2}*[(2 \space * \space 5) \space + \space (5 \space- \space1) \space * \space -0.5]\)



\(S_n = \frac{5}{2}* [10 \space - \space 2]\)



[m]S_n = 20 miles


Option B


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Re: A bicyclist begins a race at a constant rate of 10 miles per hour [#permalink] New post   07 May 2023, 04:52
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Re: A bicyclist begins a race at a constant rate of 10 miles per hour [#permalink]
07 May 2023, 04:52
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