Question

a man covers a distance of 147 km on the motor bike. he starts with speed of x kmph and doubles his speed after every 45 minutes. he has to repeat this two times to cover the distance. find the initial speed of man and also find his average speed.

Answer 1

is given that the normal speed of the motorcycle is 50km/hr50km/hr

His increased speed is 80km/hr

he has at most of 1hour's time.

Let xx and yy be the time,which we takes,when the speed is normal

∴80x+50y≤4000∴80x+50y≤4000

⇒8x+5y≤400⇒8x+5y≤400

The cost for the petrol when goes in the normal speed is Rs.2 per kms.

The cost for the petrol when goes in the increased speed is Rs.3 per kms.

He has at most of Rs 120 to spend.

∴2x+3y≤120∴2x+3y≤120

Step 2:

Let us draw the graph for the lines AB:8x+5y=400AB:8x+5y=400 and CD=2x+3y=120CD=2x+3y=120

Let us solve these two lines to find the point of intersection

8x+5y=4008x+5y=400-----(1)

2x+3y=1202x+3y=120------(2)

Multiply equ(2) by 4

8x+5y=4008x+5y=400

8x+12y=4808x+12y=480

_________________

−7y=−80−7y=−80

y=807y=807⇒x=3007⇒x=3007

Step 3:

Consider the line AB:8x+5y=400AB:8x+5y=400

Put x=0,y=0x=0,y=0 then 0≤4000≤400 which is true.

Hence the region 8x+5y≤4008x+5y≤400 lies below the line AB

Consider the line CD:2x+3y=120CD:2x+3y=120

Put x=0,y=0x=0,y=0,then 0≤1200≤120,which is true.

Hence the region 2x+3y≤4002x+3y≤400 lies below the line CD.

The region O(0,0)O(0,0) is also included in the feasible region.


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