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

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Math Expert
Joined: 02 Sep 2009
Posts: 54496
Cecile commutes from her home to her office by either driving her car  [#permalink]

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15 Jun 2017, 02:44
00:00

Difficulty:

15% (low)

Question Stats:

84% (02:22) correct 16% (02:48) wrong based on 147 sessions

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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

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

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15 Jun 2017, 02:55
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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;

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

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

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15 Jun 2017, 04:11
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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.

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

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15 Jun 2017, 13:05
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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17 Jun 2017, 05:24
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

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

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13 Aug 2017, 13:31
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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13 Aug 2017, 20:28
1
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
Re: Cecile commutes from her home to her office by either driving her car   [#permalink] 13 Aug 2017, 20:28
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