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.

Step-by-step explanation:

distance = rate times time, so

           distance

time =

               rate

Here the distance is 40 km and the rate is x.  Then

              40 km

time =  =  (40/x) hr

             x km/hr

If the speed is reduced by 2 km/hr, we get:

              40 km                                            40 km                  40

time =  or time = = hr

             (x km/hr - 2 km/hr)                      (x - 2) (km/hr)       x - 2

The difference between the times is:

 40          40

- = 1 hr          Solve this for the original speed, x

x - 2         x

40x - 40x + 80                                80

 =  1 hr     or     = 1     or 80 = x^2 - 2x

     x(x - 2)                                     x(x - 2)

Rewriting this in standard quadratic form:  x^2 - 2x - 80 = 0

Here a = 1, b = -2 and c = -80, and so the discriminant b^2 - 4ac is:

(-2)^2 - 4(1)(-80) = 324

The solutions are:

      -(-2) ± √324       2 ± 18

x = = = 1 ± 9, or 10 (discard the other root)

              2                      2

The original speed was 10 km/hr

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

she will travel a distance in the range of 3 - 11 miles