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Youseff lives x blocks from his office. It takes him 1 minute per bloc

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Youseff lives x blocks from his office. It takes him 1 minute per bloc [#permalink]

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New post 21 Sep 2015, 08:04
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Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 10 minutes more to walk to work than to ride his bike to work, then x equals?

a.4
b.7
c.10
d.15
e.20


[Reveal] Spoiler:
oa is d

I have solved it, by using backsolving but i tried one other method please tell me where am i wrong. I am not reasoning in minutes but in seconds and the result it is not the same
X/60-X/20 = 600
[Reveal] Spoiler: OA
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Re: Youseff lives x blocks from his office. It takes him 1 minute per bloc [#permalink]

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New post 21 Sep 2015, 09:08
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siriusvj wrote:
Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 10 minutes more to walk to work than to ride his bike to work, then x equals?

a.4
b.7
c.10
d.15
e.20


oa is d

I have solved it, by using backsolving but i tried one other method please tell me where am i wrong. I am not reasoning in minutes but in seconds and the result it is not the same
X/60-X/20 = 600


Please follow posting guidelines, link is in my signatures.

As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 600 (which is TIME in seconds.).

Thus the correct equation is : 60*x-20*x=600 ----> 40x=600--> x = 15.
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Re: Youseff lives x blocks from his office. It takes him 1 minute per bloc [#permalink]

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New post 21 Sep 2015, 14:59
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Hi siriusvj,

This question can be solved by TESTing THE ANSWERS.

We're given Youseff's rate to walk (1 minute/block) and bike (20 seconds/block = 1/3 minute/block) to work. We're also told that the DIFFERENCE in those two times is exactly 10 minutes. We're asked for the number of blocks between Youseff's home and work.

Since the DIFFERENCE is 10 minutes, and the walking rate is 1 minute/block, there MUST be MORE than 10 blocks (since 10 blocks = 10 minutes to walk and it takes a certain amount of time to bike, so the difference in time would be less than 10 minutes).

Let's TEST Answer D:

IF....15 blocks....
15(1 min/block) = 15 minutes to walk
15(1/3 min/block) = 5 minutes to bike
The difference IS 10 minutes, which is a MATCH for what we were told, so this MUST be the answer.

Final Answer:
[Reveal] Spoiler:
D


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Youseff lives x blocks from his office. It takes him 1 minute per bloc [#permalink]

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New post 12 Mar 2017, 13:44
Youssef lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bicycle to work. If it takes him exactly 10 minutes more to walk to work than to ride his bicycle, then x equals:

A) 4
B) 7
C) 10
D) 15
E) 20


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Last edited by Vyshak on 12 Mar 2017, 15:33, edited 1 time in total.
Topic Merged. Refer to the above discussions.
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Re: Youseff lives x blocks from his office. It takes him 1 minute per bloc [#permalink]

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New post 12 Mar 2017, 18:28
siriusvj wrote:
Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 10 minutes more to walk to work than to ride his bike to work, then x equals?

a.4
b.7
c.10
d.15
e.20



The key point to tackle the problem is to convert Time / second into a single unit.
For example, if we convert the figures in seconds, the equation could be 60x - 20x = 600.

Alternatively, if converting in minutes, we get-
x - (1/3)x = 10
or, (2/3)x = 10
or, x = 15.
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Re: Youseff lives x blocks from his office. It takes him 1 minute per bloc [#permalink]

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New post 14 Mar 2017, 04:08
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siriusvj wrote:
Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 10 minutes more to walk to work than to ride his bike to work, then x equals?

a.4
b.7
c.10
d.15
e.20


[Reveal] Spoiler:
oa is d

I have solved it, by using backsolving but i tried one other method please tell me where am i wrong. I am not reasoning in minutes but in seconds and the result it is not the same
X/60-X/20 = 600


Solved this by converting to block per second measures. So it's 1 block per 60 seconds (Rate1) and 1 block per 20 seconds (Rate2). Solving for time it's x over 1/60 = 60x and x over 1/20=20x.

Time1 - Time2 or 60x - 20x=600; (the 600 derived from 10minutes converted to seconds)
40x=600/40;
x=15.

Answer is D.
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Re: Youseff lives x blocks from his office. It takes him 1 minute per bloc [#permalink]

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New post 15 Mar 2017, 15:50
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siriusvj wrote:
Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 10 minutes more to walk to work than to ride his bike to work, then x equals?

a.4
b.7
c.10
d.15
e.20


We are given that Youseff lives x blocks from work. He can walk to work at a rate of 1 block per minute; thus, it takes him (1)(x) = x minutes to walk to work. We are also given that he can bike to work at a rate of 20 seconds per block or 20/60 = 1/3 minute per block; thus it takes him(1/3)x minutes to bike to work. Since it takes him 10 more minutes to walk to work than it does to ride, we can create the following equation to determine x:

x = (1/3)x + 10

3x = x + 30

2x = 30

x = 15

Answer: D
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Re: Youseff lives x blocks from his office. It takes him 1 minute per bloc   [#permalink] 15 Mar 2017, 15:50
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