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Cecile commutes from her home to her office by either driving her car

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Cecile commutes from her home to her office by either driving her car [#permalink]

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Cecile commutes from her home to her office by either driving her car or riding her bike. If she drives, she covers one mile in 4 minutes and and if she rides her bike she cover one mile in 9 minutes. If it takes her 30 minutes longer to ride her bike from her home to her office than to drive, how far is the distance from her home to her office?

A. 5 miles
B. 6 miles
C. 8 miles
D. 9 miles
E. 12 miles
[Reveal] Spoiler: OA

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Cecile commutes from her home to her office by either driving her car [#permalink]

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Bunuel wrote:
Cecile commutes from her home to her office by either driving her car or riding her bike. If she drives, she covers one mile in 4 minutes and and if she rides her bike she cover one mile in 9 minutes. If it takes her 30 minutes longer to ride her bike from her home to her office than to drive, how far is the distance from her home to her office?

A. 5 miles
B. 6 miles
C. 8 miles
D. 9 miles
E. 12 miles


Let Distance be D.

Speed of car = \(\frac{1}{4}\) miles/min

Let Time taken by car = t

Speed of bike = \(\frac{1}{9}\) miles/min

Time taken by bike = 30 mins longer than time taken by car = t + 30

\(D = \frac{1}{4} * t\) -------- (i)

\(D = \frac{1}{9}* (t + 30)\) ------------- (ii)

Equating (i) and (ii), we get;

\(\frac{1}{4} * t = \frac{1}{9} * (t + 30)\)

\(\frac{t}{4} = \frac{(t + 30)}{9}\)

\(9t = 4t + 120\)

\(5t = 120\)

\(t = 24\)

Substituting value of t in (i), we get;

\(D = \frac{1}{4} * 24 = 6 miles\).

Answer (B)

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Re: Cecile commutes from her home to her office by either driving her car [#permalink]

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Bunuel wrote:
Cecile commutes from her home to her office by either driving her car or riding her bike. If she drives, she covers one mile in 4 minutes and and if she rides her bike she cover one mile in 9 minutes. If it takes her 30 minutes longer to ride her bike from her home to her office than to drive, how far is the distance from her home to her office?

A. 5 miles
B. 6 miles
C. 8 miles
D. 9 miles
E. 12 miles


Speed of car = 1/4 mile/min
Speed of bike = 1/9 mile/min

Let the distance from her home to her office = x
So x/(1/9) - x/(1/4) = 30
5x = 30 -> x = 6 miles.

[Reveal] Spoiler:
Answer B

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Cecile commutes from her home to her office by either driving her car [#permalink]

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New post 15 Jun 2017, 12:05
Bunuel wrote:
Cecile commutes from her home to her office by either driving her car or riding her bike. If she drives, she covers one mile in 4 minutes and and if she rides her bike she cover one mile in 9 minutes. If it takes her 30 minutes longer to ride her bike from her home to her office than to drive, how far is the distance from her home to her office?

A. 5 miles
B. 6 miles
C. 8 miles
D. 9 miles
E. 12 miles


let t=minutes to drive
4/9=t/(t+30)
t=24 minutes
24 minutes/4 minutes per mile=6 miles
B

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Re: Cecile commutes from her home to her office by either driving her car [#permalink]

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New post 17 Jun 2017, 04:24
Bunuel wrote:
Cecile commutes from her home to her office by either driving her car or riding her bike. If she drives, she covers one mile in 4 minutes and and if she rides her bike she cover one mile in 9 minutes. If it takes her 30 minutes longer to ride her bike from her home to her office than to drive, how far is the distance from her home to her office?

A. 5 miles
B. 6 miles
C. 8 miles
D. 9 miles
E. 12 miles


We can let the distance to the office = d.

We are given that Cecile’s driving rate is 1/4 mile/minute and her biking rate is 1/9 mile/minute.

Thus, her driving time is d/(1/4) = 4d and her biking time is d/(1/9) = 9d.

Since it takes her 30 more minutes to bike than to drive, we have:

9d = 4d + 30

5d = 30

d = 30/5 = 6

Answer: B
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Re: Cecile commutes from her home to her office by either driving her car [#permalink]

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New post 13 Aug 2017, 12:31
Bunuel wrote:
Cecile commutes from her home to her office by either driving her car or riding her bike. If she drives, she covers one mile in 4 minutes and and if she rides her bike she cover one mile in 9 minutes. If it takes her 30 minutes longer to ride her bike from her home to her office than to drive, how far is the distance from her home to her office?

A. 5 miles
B. 6 miles
C. 8 miles
D. 9 miles
E. 12 miles


The only thing with this one is that you have to use fractions, but nonetheless it is very much like an overtake question- in overtake questions the distance traveled is the same so

D=RT or D=ST
Distance between home and office = 1 minute/ 4 miles (x)

1/4x = 1/9x (x+30) set them equal

1/4x = 1/9x +30/9

120/36=5/36

120/5= 24

1/4(24) =6

B

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Re: Cecile commutes from her home to her office by either driving her car [#permalink]

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New post 13 Aug 2017, 19:28
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every 1 mile she rides on bike, will take her extra 5 minutes (9min-4min).
so if she take 30 minutes longer, it is 30/5= 6 miles

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Re: Cecile commutes from her home to her office by either driving her car   [#permalink] 13 Aug 2017, 19:28
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