Question 1112488
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.