Question

The distance covered by a bike is given by the expression 2x² +6x -20. The time taken by the bike to covered this distance is given by the expression x - 2. Find the speed of the bike.

Answer 1

Answer:

distance ,s=2x² +6x -20

time taken,t=x - 2

speed=ds/dt

so,ds/dx= 4x+6....eq(1)

and dt/dx =1.....eq(2)

by dividing eq(1) by (2)

we get,

ds/dt=4x+6

so, the speed of bike is 4x+6

Answer 2

The speed of the bike = 2x + 10

Given :

• The distance covered by a bike is given by the expression 2x² + 6x -20.
• The time taken by the bike to covered this distance is given by the expression x - 2

To find : The speed of the bike

Solution :

Here distance covered by a bike is given by the expression 2x² + 6x -20.

The time taken by the bike to covered this distance is given by the expression x - 2

Total distance travelled = 2x² + 6x -20

Total time taken = x - 2

The speed of the bike

$\displaystyle \sf{ = \frac{2 {x}^{2} + 6x - 20 }{x - 2} }$

$\displaystyle \sf{ = \frac{2 ({x}^{2} + 3x - 10) }{x - 2} }$

$\displaystyle \sf{ = \frac{2 [{x}^{2} + (5 - 2)x - 10] }{x - 2} }$

$\displaystyle \sf{ = \frac{2 [{x}^{2} + 5x - 2x - 10] }{x - 2} }$

$\displaystyle \sf{ = \frac{2 [x(x + 5) - 2(x + 5)] }{x - 2} }$

$\displaystyle \sf{ = \frac{2 (x + 5) (x- 2) }{x - 2} }$

$\displaystyle \sf{ = 2(x + 5) }$

$\displaystyle \sf{ = 2x + 10 }$

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