Problem Solving

To this day - I still do not have a fast method of doing VICS rates and work. I know to pick numbers - but I always end up picking really bad #'s. Can someone walk me through a method - to conquer this. It would probably take me 3.5 - 4 minutes to do this problem and I would like to do it in 2.5 if not 2.

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. (12000) / x+200

(E)

There are lots of ways

Lets take X =50 , why do we take X = 50 because x is a variable and X can take any value from 1 to 99 ( because x is a % and that there is x and 100-x , so x can take from 1 to 99 )

If x is 50 then F travels 1/2 the distance @ 40 and 1/2 @ 60 so we can easily find the average speed for the total distance traveled


Avg speed = 48

Look at the answer choices , substitute x in the following

A. (180 - x) / 2 : too big
B. (x+60) / 4 : Too small
C. (300 - x) / 5 : Big
D. (600) / 115 - x : Small
E. (12000) / x+200 : left with this only

So answer is E

Method II

take the total distance as d

so the average = tot distance / tot time

But the total time is in two parts

Total time = d*x/4000 + d*(100-x)/6000

= d(2000x +4000*100)/ 4000*6000

= d(x+200)/12000

So the average = d/ d(x+200)/12000

= 12000/(x+200) = E

ghacker wrote:There are lots of ways

Lets take X =50 , why do we take X = 50 because x is a variable and X can take any value from 1 to 99 ( because x is a % and that there is x and 100-x , so x can take from 1 to 99 )

If x is 50 then F travels 1/2 the distance @ 40 and 1/2 @ 60 so we can easily find the average speed for the total distance traveled


Avg speed = 48

Look at the answer choices , substitute x in the following

A. (180 - x) / 2 : too big
B. (x+60) / 4 : Too small
C. (300 - x) / 5 : Big
D. (600) / 115 - x : Small
E. (12000) / x+200 : left with this only

So answer is E

Method II

take the total distance as d

so the average = tot distance / tot time

But the total time is in two parts

Total time = d*x/4000 + d*(100-x)/6000

= d(2000x +4000*100)/ 4000*6000

= d(x+200)/12000

So the average = d/ d(x+200)/12000

= 12000/(x+200) = E

Great I used method 1. I like it - but so do you typically choose 50? I guess - I typically spend 20-30 seconds figuring out which number to pick.

actually u could select X= 40 also ; then it would be easier since I like 50 I selected 50 . It depends on the person