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Bob bikes to school every day at a steady rate of x miles

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Bob bikes to school every day at a steady rate of x miles [#permalink] New post 12 Sep 2008, 16:48
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Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?

A. (x + y) / t

B. 2(x + t) / xy

C. 2xyt / (x + y)

D. 2(x + y + t) / xy

E. x(y + t) + y(x + t)

OPEN DISCUSSION OF THIS QUESTION IS HERE: bob-bikes-to-school-every-day-at-a-steady-rate-of-x-miles-57035.html
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Re: mgmat [#permalink] New post 12 Sep 2008, 18:46
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IMO C

Let distance be S ;

so , bob cycled S/2 => S/2= x*t1 ( t1= time taken to cycle ) => t1=S/2x
and S/2 = y*t2 ( t2 is time taken to walk ) => t2 = S/2y

now t1 + t2 = t
=> S/2x + S/2y= t => S* ( x+y)/2xy = t=> S= 2xyt/( x+y)
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Re: mgmat [#permalink] New post 09 Feb 2013, 09:47
ssandeepan wrote:
IMO C

Let distance be S ;

so , bob cycled S/2 => S/2= x*t1 ( t1= time taken to cycle ) => t1=S/2x
and S/2 = y*t2 ( t2 is time taken to walk ) => t2 = S/2y

now t1 + t2 = t
=> S/2x + S/2y= t => S* ( x+y)/2xy = t=> S= 2xyt/( x+y)


I don't get this question.
Normally I just use the pick-a-number-approach.

If we choose for d (distance): 10 miles, for x 10 and for y 5.
t would be 90 minutes or 1,5 hours.

If I try this for answer choice A it fits.

Can anyone explain what I am doing wrong?

Many thanks.
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Re: mgmat [#permalink] New post 10 Feb 2013, 02:46
waltiebikkiebal wrote:
ssandeepan wrote:
IMO C

Let distance be S ;

so , bob cycled S/2 => S/2= x*t1 ( t1= time taken to cycle ) => t1=S/2x
and S/2 = y*t2 ( t2 is time taken to walk ) => t2 = S/2y

now t1 + t2 = t
=> S/2x + S/2y= t => S* ( x+y)/2xy = t=> S= 2xyt/( x+y)


I don't get this question.
Normally I just use the pick-a-number-approach.

If we choose for d (distance): 10 miles, for x 10 and for y 5.
t would be 90 minutes or 1,5 hours.

If I try this for answer choice A it fits.

Can anyone explain what I am doing wrong?

Many thanks.


For plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

OPEN DISCUSSION OF THIS QUESTION IS HERE: bob-bikes-to-school-every-day-at-a-steady-rate-of-x-miles-57035.html
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Re: mgmat   [#permalink] 10 Feb 2013, 02:46
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