SOLUTION: A man is travelling at 20km/hr. How much time would he save if instead of going north then west, he goes in a straight line? Thank you!

Question 1112488: A man is travelling at 20km/hr. How much time would he save if instead of going north then west, he goes in a straight line?
Thank you!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
he's traveling at 20 km per hour.

if he goes north and then west, he's traveling along the legs of a right triangle.

if he goes straight, he's traveling along the hypotenuse of the right triangle.

the hypotenuse of a right triangle is equal to the square root of the sum of the legs squared.

if the hypotenuse is c, and the legs are a and b, then c = square root of (a^2 + b^2).

rate * time = distance.

his rate is 20 kilometers per hour.

formula becomes 20 * time = distance.

if the distance going north and west is equal to a + b, and the distance going straight is square root of (a^2 + b^2), then, the distance he saves will be square root of (a^2 + b^2) / (a + b)

going north and then west, the formula of rate * time = distance becomes:

20 * time = (a + b)

going straight, the formula of rate * time = distance becomes:

20 * time = square root of (a^2 + b^2)

if you solve for time in both of these equations, you will get:

time for north and then west = (a + b) / 20

time for straight = sqrt(a^2 + b^2) / 20

the amount of time he saves will be:

(a + b) / 20 minus sqrt(a^2 + b^2) / 20

since the denominator is the same, this can be shown as:

the amount of time he saves will be:

(a + b - sqrt(a^2 + b^2)) / 20

to find the time he saves, you need to know the value for a and b.

then you can calculate the value for sqrt(a^2 + b^2).

for example:

assume he travels 10 miles north and 20 miles west.

the formula of (a + b - sqrt(a^2 + b^2)) / 20 becomes:

((10 + 20) - sqrt(a^2 + b^2)) / 20

evaluate this formula to get:

time he saves = .3819660113 hours.

let's see if this makes sense.

going north and west is a total of 30 miles.

rate * time = distance

20 * time = 30

solve for time to get:

time = 30/20 = 1.5 hours.

that's how long it takes going north and west.

if he goes straight, the distance is sqrt(10^2 + 20^2).

that's a total of 22.36067977 miles

rate * time = distance becomes:

20 * time = 22.36067977 miles

solve for time to get time = 22.36067977 / 20 = 1.118033989 hours.

difference between 1.5 hours and 1.118033989 hours is .3819660113 hours.

formula is good.

to find the time saved, you need to know the values of a and b.

without knowing that, you have insufficient evidence to determine how much time is saved.

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