An increase of speed of 4 km/h on a journey of 32 km reduces
the time taken by 4 hours. find the original speed.

Let s = original speed

then

(s+4) = the faster speed

:

Write time equation; time = distance%2Fspeed

:

original speed time - 4 hr = faster speed time

32%2Fs - 4 = 32%2F%28%28s%2B4%29%29

:

Multiply equation by s(s+4), results:

32(s+4) - 4s(s+4) = 32s

:

Multiply what's inside the brackets

32s + 128 - 4s^2 - 16s = 32s

:

-4s^2 - 16s + 128 = 0; subtracted 32s from both sides,

:

Simplify, change the signs, divide equation by -4

s^2 + 4s - 32 = 0

Factor

(s + 8)(s - 4) = 0

Positive solution

s = 4 km/hr is the original speed

:

:

Check solution finding the time of each (faster speed = 8 km/hr)

32/4 = 8 hrs

32/8 = 4 hrs

differ 4 hrs

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

x = 23.78

step-by-step explanation: