Zachary travels on a journey of 50 miles. He spends half
of his time riding his horse and half of his time walking.
When he rides his horse, he covers 9 miles every hour.
When he walks, he covers 3 1⁄2 miles every hour. How
much time does it take him to complete the journey?

8 hours.

Step-by-step explanation:

We have the relation:

Time  = distance/velocity

Distance = 50 miles

Velocity in horse = 9mph

Velocity walking = 3 1/2 mph = 3.5 mph

Then, if T is the total time, X is the distance that he travels in horse and Y is the distance that he travels by foot, we have:

X + Y = 50 miles:

T/2 = X/9mph

T/2 = Y/3.5mph

Then we have:

X/9mph = Y/3.5mph

X = Y*(9/3.5)

And by the first relation:

X = 50 mi - Y

then we have:

50mi - Y = Y*(9/3.5)

50mi = Y + Y*(9/3.5) = Y*(1 + 9/3.5) = Y*3.57

Y = 50mi/3.57 = 14mi

Then we have:

T/2 = 14mi/3.5mph

T = 2*(14/3.5) hours = 8 hours

yes yes yes yes yes yes yes yes yes

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.