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At the rate of x feet per s seconds, how many miles does a cyclist tr

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At the rate of x feet per s seconds, how many miles does a cyclist tr  [#permalink]

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15 Jan 2017, 17:47
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71% (02:02) correct 29% (02:49) wrong based on 83 sessions

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At the rate of x feet per s seconds, how many miles does a cyclist travel in y minutes(5280 feet per mile)?

a) xy/88s
b) 88s/xy
c) xy/5280s
d) 5280s/xy
e) 15xy/22s

Please help me understand how to approach above conversion problems. Source is Veritas Prep Book on word problems.

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At the rate of x feet per s seconds, how many miles does a cyclist tr  [#permalink]

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15 Jan 2017, 20:14
1
anairamitch1804 wrote:
At the rate of x feet per s seconds, how many miles does a cyclist travel in y minutes(5280 feet per mile)?

a) xy/88s
b) 88s/xy
c) xy/5280s
d) 5280s/xy
e) 15xy/22s

Please help me understand how to approach above conversion problems. Source is Veritas Prep Book on word problems.

anairamitch1804

distance = Rate(speed)*time
given rate = x feet/ s sec
time = y minutes
as 5280 ft = 1 mile
thus x ft = x/5280 miles
again 1 minute has 60 sec
So 1 sec has 1/60 minutes
or s sec has s/60 minutes
thus rate = x/5280 miles / s/60 minutes
60x/5280s miles /minute

thus distance travelled in y minutes
= 60x/5280s miles /minute *y minutes
=xy/88s

Ans A
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Posts: 58453
Re: At the rate of x feet per s seconds, how many miles does a cyclist tr  [#permalink]

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16 Jan 2017, 01:07
1
anairamitch1804 wrote:
At the rate of x feet per s seconds, how many miles does a cyclist travel in y minutes(5280 feet per mile)?

a) xy/88s
b) 88s/xy
c) xy/5280s
d) 5280s/xy
e) 15xy/22s

Please help me understand how to approach above conversion problems. Source is Veritas Prep Book on word problems.

Check other Conversion problems to practice from our Special Questions Directory.
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Re: At the rate of x feet per s seconds, how many miles does a cyclist tr  [#permalink]

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18 Jan 2017, 11:04
1
3
anairamitch1804 wrote:
At the rate of x feet per s seconds, how many miles does a cyclist travel in y minutes(5280 feet per mile)?

a) xy/88s
b) 88s/xy
c) xy/5280s
d) 5280s/xy
e) 15xy/22s

We need to determine the number of miles a cyclist can travel in y minutes at the rate of x feet per s seconds.

First, we convert y minutes to seconds:

y minutes = 60y seconds

Since rate x time = distance, the cyclist travels (x/s)(60y) = 60xy/s feet in y minutes.

Now, we convert feet to miles:

(60xy/s)/(5280) = (60xy)/(5280s) = (xy)/(88s)

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Re: At the rate of x feet per s seconds, how many miles does a cyclist tr  [#permalink]

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18 Jan 2018, 16:35
Hi All,

These types of questions can almost always be beaten by TESTing VALUES and staying really organized with your work. The formatting of the answer choices is also important - here, the answers are designed in such a way that you don't have to perform every calculation to prove whether an answer is correct or not (and that 'option', when it appears, can play a big role in how effective you are with your overall pacing).

With these answers, notice how a couple of the answers 'hinge' on the number 5280, while two others hinge on the number 88 and the last hinges on the number 22. When TESTing VALUES, you might consider TESTing relatively small values and taking advantage of the patterns in the answer choices.

IF we TEST
X = 3
S = 2
Y = 1

At a rate of 3 feet per 2 seconds, how many miles does a cyclist travel in 1 minute....

1 minute = 60 seconds

60 seconds/2 seconds = 30... so the cyclist traveled (3 feet)(30) = 90 feet in 1 minute. However, this question asks for the number of MILES that the cyclist traveled in Y minutes... and 90 feet is a TINY FRACTION of a mile (specifically 90/5280 = 9/528 = 3/176).

Since all 3 variables are small integers, you can eliminate certain answers immediately...

Answer B = 88..../..... = this will be far GREATER than 1.
Answer C = (3)(4)/(5280)(1) = 12/5280.... this is far TOO SMALL
Answer D = 5280..../..... = this will be significantly GREATER than 1

That just leaves two answers remaining (and notice how the variables appear in the same 'positions' in both answers, but the numerators and denominators are multiplied by different integers). If either answer matches, then you'd have the correct one...

Answer A = (3)(1)/(88)(2) = 3/176

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Rich
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Re: At the rate of x feet per s seconds, how many miles does a cyclist tr   [#permalink] 18 Jan 2018, 16:35
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