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

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step-by-step explanation: