Problem Solving

I have a tough time deciding which variables to choose smart numbers for and also which ones to call x. How do you all decide which variables are the unknowns and which ones you solve for?

An example questions follows:

Is there a good strategy for knowing where to put these variables?
During a trip, Francine traveled x percent of the total
distance at an average speed of 40 miles per hour
and the rest of the distance at an average speed of
60 miles per hour. In terms of x, what was Francine's
average speed for the entire trip?

(A) (180 - x) / 2
(B) (x + 60) / 4
(C) (300 - x) / 5
(D) 600 / (115 - x)
(E) 12,000 / (x + 200)

correct answer is E

are you sure your not missing something from the answers or the question?

can you please confirm.

this is how i am doing it though....

lets say total distance = 240 miles (i picked 240 because is a common multiple of 40,60 -- pick numbers like this)

x% of total distance @ 40mph - so Let x be 50%.
So,

120 miles @ 40mph - drove for 3 hours
120 miles @ 60mph - drove for 2 hours

r = d/t

r=240/5 = 48mph < avg speed

now if i plug in the same numbers into the answers, i am not getting a correct answer for any one of the options.

am i doing something wrong?

Let total distance be 100

First part

D=x/100*100=x

S=40 miles/hr

T=x/40

Second part

D=(100-x)/100*100=100-x

S=60 miles/hr

T=100-x/60

Average Speed=Total distance/total time taken

=x+100-x/(x/40+(100-x)/60)


=100/(60x+4000-40x)/2400

=240000/(20x+4000)

=12000/(x+200)

Pick E

Gurpinder wrote:are you sure your not missing something from the answers or the question?

can you please confirm.

this is how i am doing it though....

lets say total distance = 240 miles (i picked 240 because is a common multiple of 40,60 -- pick numbers like this)

x% of total distance @ 40mph - so Let x be 50%.
So,

120 miles @ 40mph - drove for 3 hours
120 miles @ 60mph - drove for 2 hours

r = d/t

r=240/5 = 48mph < avg speed

now if i plug in the same numbers into the answers, i am not getting a correct answer for any one of the options.

am i doing something wrong?

Hey dude..

Note that average speed is not average of 2 speeds.

Average speed=Total distance/Total time taken

Now as per ur steps,

AS=240/(2+3)=240/5=48

Plug x=50 in option E

12000/(250)=48

Hope this clarify!

selango wrote:
Hey dude..

Note that average speed is not average of 2 speeds.

Average speed=Total distance/Total time taken

Now as per ur steps,

AS=240/(2+3)=240/5=48

Plug x=50 in option E

12000/(250)=48

Hope this clarify!

hey,
isnt that what i did?

total d = 240
total time = 5 hrs
so total avg speed = 240/5

and how are you getting x = 50?

thx

Oh u mentioned that 48<avg speed.

Ok then what u did is correct.

X is % value.As per ur case you assumed x=50

So plug in 50 in options and check the value.

selango wrote:Oh u mentioned that 48<avg speed.

Ok then what u did is correct.

X is % value.As per ur case you assumed x=50

So plug in 50 in options and check the value.

lol.

alright that works.

so on a problem like this, arent you suppose to enter the actual value rather than %? why % value?

Also, i've read in MGMAT books that when you do enter % value, it should be in decimals. so .50? what about that?

thx

1uponGMAT wrote:I have a tough time deciding which variables to choose smart numbers for and also which ones to call x. How do you all decide which variables are the unknowns and which ones you solve for?

An example questions follows:

Is there a good strategy for knowing where to put these variables?
During a trip, Francine traveled x percent of the total
distance at an average speed of 40 miles per hour
and the rest of the distance at an average speed of
60 miles per hour. In terms of x, what was Francine's
average speed for the entire trip?

(A) (180 - x) / 2
(B) (x + 60) / 4
(C) (300 - x) / 5
(D) 600 / (115 - x)
(E) 12,000 / (x + 200)

correct answer is E

The trick is to plug in values that make the math easy.

For the distance traveled at 40mph, plug in a multiple of 40:
d = 80 miles
r = 40 mph
t = d/r = 80/40 = 2 hrs

For the distance traveled at 60 mph, plug in a number that is a multiple not only of 60 but also of 80 (the first distance). Using a multiple of 80 will make it easy later on to determine the value of x:
d = 240 miles
r = 60 mph
t = 240/60 = 4 hrs

First part of the trip = 80 miles.
Total distance = 80+240 = 320 miles.
Since 80 is 25% of 320, x = 25. (See how using a multiple of 80 for the second distance made it easy to determine x?)

Now that we have assigned values to everything, let's get our target:
Total distance = 80+240 = 320 miles
Total time = 2+4 = 6 hrs
Average rate = 320/6 = 160/3. This is our target answer.

Now we plug x=25 into all the answers to see which give us 160/3:

(A) (180 - x) / 2 = (180-25)/2 = 155/2. No.
(B) (x + 60) / 4 = (25+60)/4 = 85/4. No.
(C) (300 - x) / 5 = (300-25)/5 = 275/5 = 55. No.
(D) 600 / (115 - x) = 600/(115-25) = 600/90 = 60/9 = 20/3. No.

The correct answer is E.

(E) 12,000 / (x + 200) = 12000/(25+200) = 12000/225 = 2400/45 = 800/15 = 160/3. This works.

I realy don't get this solution.

Suppose Time =100
Then the traveled distance would be: D=40x + (100-x)60 = 6000 - 20x
If R=D/T then
(6000 - 20x) / 100 = R = (300 - x)/5
hence answer c.

Check:
x=25
D1 = 25*40 = 1000
D2 = (100-25)*60 = 4500
1000+4500=5500
R=5500/100=55M/h
or
(300-x)/5 = (300-25)/5=55
OK

x=20
D1 = 20*40 = 800
D2 = (100-20)*60 = 4800
800+4800=5600
R=5600/100=56M/h
or
(300-x)/5 = (300-20)/5=56

So why should answer c be wrong?