Expert: Josh - 6/29/2007

Question
QUESTION: while driving to houston sumiran drives 1st one and half hour at a constant speed of 70 miles/hour. reducing her speed by 1/7th she travels another 60 miles in an hour. if she had to reach houston in 4 hours. with what speed should she drive, given that houston is 400 miles from dallas

ANSWER: Hello,

The total distance D=400 miles must be covered in T hours. T=T1+T2+T3, where T1=1.5 hours, T2=1 hour and T3=4 hours. Given the speed at which the vehicle is travelling in each time period, we can work out the distance covered during each period.

Let V1=70 mile/hour, V2=V1*(1-1/7)=V1*(6/7), V3=? be the speed of the vehicle during these periods.

The basic principle is that
-----------------------------------------------------
 Distance Travelled = Speed x Time Duration. (#)
-----------------------------------------------------

For example,
D1=V1*T1
 =70*1.5
 =105 [miles]

D2=V2*T2
 =V1*(6/7)*1
 =70*(6/7)*1
 =60 [miles]

The remaining distance D3=D-(D1+D2)=400-(105+60)=235 [miles]

From the formula above (#), speed = distance/time.

Therefore, the required speed in the third part of the journey is given by
V3=D3/T3
 =235/4
 =58.75 mile/hour


---------- FOLLOW-UP ----------

QUESTION: in sumiran's mp3 player she has 64 mb free space. if she has 10-6 mb and 10-5 mb songs. what will be the best combination to put maximum number of songs with atleast 5 6 mb songs

Answer
We have to find "x" and "y" (i.e., x 5 Mb songs and y 6 Mb songs) such that 5x+6y is maximized, subject to the constraints, 5x+6y<=B, B=64; x<=10, y<=10 and y>=5.

Draw these lines in the x-y plane, and shade in the region where these conditions are satisfied. The objective is to find integer numbers, x and y, as close to the line 5x+6y=B as possible (i.e., using the memory space to the fullest extent).

By trial-and-error, we find that
When x=5,y=5, 5x+6y=55.
When x=5,y=6, 5x+6y=61. <= optimal solution *
When x=5,y=7, 5x+6y=67 NOT a solution.
When x=6,y=5, 5x+6y=60.
When x=7,y=5, 5x+6y=65 NOT a solution