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distance time

by canuckclint » Tue Nov 04, 2008 9:46 pm
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?

(x + y) / t


2(x + t) / xy


2xyt / (x + y)


2(x + y + t) / xy


x(y + t) + y(x + t)
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by cramya » Tue Nov 04, 2008 9:56 pm
I think its been solved here before but cant find the link

Since variables appear in the question and answer choices pick easy numbers

Let x=4 y=2 t=12

d/2/4 + d/2/2 = 12 (Distance/speed in first half+ Distance/speed in first half gives total time

d=32


Susbtitute x,y and t values in the answer choices and the only one that works is C)2xyt / (x + y)
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Re: distance time

by logitech » Tue Nov 04, 2008 10:01 pm
canuckclint wrote: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?

(x + y) / t


2(x + t) / xy


2xyt / (x + y)


2(x + y + t) / xy


x(y + t) + y(x + t)
so lets call the half of the distance a

so

t= t-bike + t-walk

t= (a/x) + (a/y)

if we solve for a, which is the half of the distance:

a= txy/(y+x)

and if you multiply this by 2, you will find the total distance

2txy/(y+x)
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Re: distance time

by canuckclint » Sun Dec 07, 2008 1:25 pm
logitech wrote:
canuckclint wrote: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?

(x + y) / t


2(x + t) / xy


2xyt / (x + y)


2(x + y + t) / xy


x(y + t) + y(x + t)
so lets call the half of the distance a

so

t= t-bike + t-walk

t= (a/x) + (a/y)

if we solve for a, which is the half of the distance:

a= txy/(y+x)

and if you multiply this by 2, you will find the total distance

2txy/(y+x)

This seems more logical but can you solve it this way:
I set up two equations...

1. t=t1+t2
2. d = xt1 + yt2
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by canuckclint » Sun Dec 07, 2008 1:59 pm
cramya wrote:I think its been solved here before but cant find the link

Since variables appear in the question and answer choices pick easy numbers

Let x=4 y=2 t=12

d/2/4 + d/2/2 = 12 (Distance/speed in first half+ Distance/speed in first half gives total time

d=32


Susbtitute x,y and t values in the answer choices and the only one that works is C)2xyt / (x + y)
This seems like the easiest way to go!
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by ab.fakhry » Tue Oct 30, 2012 9:25 pm
Why i cannot just say:

since the distance was "exactly halfway", then the average rate = (x+y)/2

Then the total distance = t * (x+y)/2

I feel that's correct, is it?
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by GMATGuruNY » Wed Oct 31, 2012 10:23 am
ab.fakhry wrote:Why i cannot just say:

since the distance was "exactly halfway", then the average rate = (x+y)/2
When the same distance is traveled at two different speeds, the average speed for the entire trip is not the average of the two speeds.
The reason is that traveling at the slower speed takes LONGER, with the result that MORE TIME is spent traveling at the SLOWER speed than at the faster speed.
Since more time is spent traveling at the slower speed, the average speed for the entire trip will be LESS than the average of the two speeds.

To illustrate:
Let the total distance = 80 miles, the slower speed = 10 miles per hour, and the faster speed = 40 miles per hour.
Time to travel half the distance at 10 miles per hour = 40/10 = 4 hours.
Time to travel half the distance at 40 miles per hour = 40/40 = 1 hour.
Average speed for the entire 80 miles = 80/5 = 16 miles per hour.
Since the average of the two speeds = (10+40)/2 = 25, the average speed for the entire trip -- 16 miles per hour -- is LESS than the average of the two speeds.
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