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

c

step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet