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## At the rate of x feet per s seconds, how many miles does a c

tagged by: ceilidh.erickson

# This topic has 8 expert replies and 2 member replies

#### At the rate of x feet per s seconds, how many miles does a c

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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I have always found that the easiest way to do unit conversions - and to make sure that you don't perform the wrong operation - it to set them up as fractions. Make sure that the unit you want to get rid of appears in the numerator of one fraction and the denominator of the other, so we can cancel it, just as we would with a variable (e.g. x/x).

For example, here's how to convert 180 min into hours:

Now, (min/min) will cancel:

For the question you posted, you have two options:

1) PICK SMART NUMBERS.
I'll choose a rate of 100 feet every 10 seconds. Now I'll set up 2 more fractions: feet to miles and seconds to minutes. I set up these fractions so that feet and seconds will cancel out:

Now, cancel the units and simplify:

We're looking for an answer of 10 miles when we plug in x = 100, s = 10, y = 88:

a) xy/88s --> (100)(88)/(88)(10) = 10. Yes!

b) 88s/xy --> 88(10)/(100)(88) = 1/10. No.

c) xy/5280s --> (100)(88)/5280(10) = 6. No.

d) 5280s/xy --> 5280(10)/(100)(88) = 1/6. No.

e) 15xy/22s --> (15)(100)(88)/(22)(10) = 600. No.

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Strategy #2: USE ALGEBRA.

Often picking smart numbers is more efficient, but in this case, it's less work to just set up the fractions using x and s, rather than picking numbers. Set up the fractions the same way we did before:

Now we can cancel our units:

When we simplify and add in a y for the number of minutes, it reduces to xy/88s miles.

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Thanks Eric for sharing multiple approaches to such kind of problems.

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You're very welcome! (The name is Ceilidh, though. Erickson is my last name).

Good luck!

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Hi Anaira Mitch,

As Ceilidh has pointed out, 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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Anaira Mitch 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.
Speed = x/s feet/sec
Time = y minute = (60 y) sec
Distance traveled = (x/s)(60y) feet = 60xy/5280s miles = xy/88s miles. (A)is correct

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Anaira Mitch 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.
This is a typical Speed/Time/Distance problem.

Here, rate can be taken as Speed.

Thus, Speed = (x/s) feet/second

Distance = Speed*Time = (x/s) feet/second * y minutes

Distance = (x/s) feet/second * (y*60) seconds

Distance = (60xy)/s feet; 'second' cancells

Since the question wants the answer in miles, we need to convert feet into miles.

We are given that '5280 feet = 1 mile.'

Thus, Distance = [(60xy)/s] *[1/5280] miles

Distance = (60xy) / (5280s) miles

Distance = xy/88s miles

Hope this helps!

-Jay
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Anaira Mitch 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
Plug in values for the SMALLER UNITS (feet and seconds) that convert easily to the LARGER UNITS (miles and minutes).
Let x = 5280 feet = 1 mile.
Let s = 60 seconds = 1 minute.
Resulting rate = 1 mile per minute.
Let y = 10 minutes.
Since the rate = 1 mile per minute, the distance traveled in y=10 minutes is 10 miles. This is our target.

Now plug x=5280, s=60 and y=10 into the answers to see which yields our target of 10.
Only A works:
xy/88s = (5280*10)/(88*60) = 5280/528 = 10.

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ceilidh.erickson wrote:
You're very welcome! (The name is Ceilidh, though. Erickson is my last name).

Good luck!
Of course, at some point in the distant past, there must have been some Eric responsible for continuing your family tree -- though to be GMATy about it, I guess I'm assuming Erickson is not a married name -- so maybe OP is thanking him for ensuring that you made it to this world and could give such clear answers on this forum

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Anaira Mitch 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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