Question

an aeroplane travelled a distance of 400km at an average speed of x km/hr.On the return journey,the speed was increased by 40km/hr .Write down an expression for the time taken for:- 1.THE ONWARD JOURNEY 2.THE RETURN JOURNEY if the return journey took 30 min less than the onward journey ,write down an equation in x and find its value

Answer 1

The expression for the onward journey: 

Speed = distance/time travelled

Time taken = distance travelled/speed

1)the expression will be :

distance/speed    =   400km     =   400/x hrs
                                  xkm/hr

2) the expression for the return journey:
distance = 400km
speed= (x + 40)km/hr

time= 400 km         =    400  hrs        
          x + 40km/hr       x+ 40

3)if the return journey took 30 minute less:

then,     400/x+40 hrs + 1/2 hr = 400/x hrs
          400x + x² + 40 x = 800x + 1600
                x² - 360x - 1600= 0....the equation

find value of x:
x² - 360x -1600 = 0
can also be written as;    x² - 400x + 40x - 1600=0
                                        x(x-400) + 40(x-400)=0
                                       (x+40)(x-400)=0
Therefore either x + 40 = 0   or x -400 = 0
Hence x is either = -40 or 400
                                       Therefore x = 400km/hr 

Answer 2

Answer:

X = 160 Km/ hr

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