HELP: Rates and Work Question! (using SmartNumbers)

[hungraa]

Hi All,

Was doing the Manhattan GMAT CAT and came across this question:

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) **Correct Answer**


D 2(x + y + t) / xy


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


On my first attempt at this question I used

x= 2 mph
y= 1 mph
total distance = 8 miles

The bike breaks down halfway so calculating time would be 4 miles bike and 4 miles walking.

So solving for t it would be 2 hours on a bike (2mph for 4 miles) and then 4 hours walking (1mph for 4 miles)

t = 6 hours

So plugging these smart numbers in:

A) Not 8 miles
B) DOES BECOME 8 miles
C) ALSO IS 8 miles
D) E) not necessary


Why is it that these set of smart numbers produce the same answer? I'd like to think for smart numbers it shouldn't matter what you pick.

I tried other smart numbers where total distance is 4 miles or 12 miles. It all works out fine where B is not the correct answer.

Please advise. Thank you all!

[GMATGuruNY]

Hi All,

Was doing the Manhattan GMAT CAT and came across this question:

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) **Correct Answer**


D 2(x + y + t) / xy


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


On my first attempt at this question I used

x= 2 mph
y= 1 mph
total distance = 8 miles

The bike breaks down halfway so calculating time would be 4 miles bike and 4 miles walking.

So solving for t it would be 2 hours on a bike (2mph for 4 miles) and then 4 hours walking (1mph for 4 miles)

t = 6 hours

So plugging these smart numbers in:

A) Not 8 miles
B) DOES BECOME 8 miles
C) ALSO IS 8 miles
D) E) not necessary


Why is it that these set of smart numbers produce the same answer? I'd like to think for smart numbers it shouldn't matter what you pick.

I tried other smart numbers where total distance is 4 miles or 12 miles. It all works out fine where B is not the correct answer.

Please advise. Thank you all!

For PS word problems with variables in the answers, avoid plugging in 1.
By plugging in y=1, you rendered the value of y irrelevant in answer choice B (since xy = x*1 = x).
If we plug in x=4, y=2, and a total distance of 8 miles -- with the result that t=3 -- then only answer choice C yields our target of 8 miles.

[theCodeToGMAT]

For Question in which normal Algebraic solution is possible try avoiding Value Plugins.

In the Question:

t = ( (D/2)/x + (D/2)/y)
D = t (2xy) (X + y)

This method could have saved sooo much time.