12. A cyclist travels 40 km at a speed of x km/h. Find the time taken in terms of x. Find the time taken when his speed is
reduced by 2 km/h. If the difference between the times is
1 hour, find the original speed x.

Answer

original speed X=10

Step-by-step explanation:

We know that Speed= distance/ time

Then

time =distance/speed

We were told the cyclist travels 40 km at a speed of x km/h.

Which means

Distance= 40km

speed =x km/h

Then time t =40/x

Again we we were told his speed was

reduced by 2 km/h

Then speed= (x-2)

But the Distance is still 40km

But we were told the difference in time is 1 hour

Time t=40/(x-2)

Then if we find the difference between the time t of the first condition and second condition we have

40/(x-2) - (40/x) =1

[40x-40(x-2)]/ x(x-2)= 1

80=x(x-2)

x^2-2x-80=0

This is a quadratic equation , if we solve using factorization we have

(x+8)(x-10)

x+8=0 or x-10= 0

X= -8 or 10

But we cannot have a negative value for speed then

X=10

Therefore, original speedX=10

(4,5

look up a corrdinate plane and do what the thingy says and boom

2.

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