John is trying to get from point A to point C, which is 20 miles away to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?
ABC is a right angled triangle right angled at B. AC = 20.
(1) The ratio of the distance going north to the distance going east is 4 to 3
By Pythagorean theorem: Let sides are 4x, 3x and 20
\(4x^2 + 3x^2 = 20^2\)
Solving, x = 4
Sides are 16, 12 and 20. Difference = 16 + 12 - 20 = 8.
SUFFICIENT.
(2) The distance traveled north going the direct route is 16
By Pythagorean theorem: Let sides are 16, x' and 20
\(16^2 + x'^2 = 20^2\)
Solving, x' = 12
Sides are 16, 12 and 20. Difference = 16 + 12 - 20 = 8.
SUFFICIENT.
Answer D.
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