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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