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?

Answer: 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