Question

a car travels along a straight road heading east for one hour, then traveling for 30 minutes on another road that leads northeast. if the car has maintained a constant spead of 40 miles per hour, how far is it from the starting position/

Answer 1

Answer:

55.96 miles

Step-by-step explanation:

Distance = Speed X time

Car first moved east for 1 hr , distance = 40 x 1 = 40 miles

Car then moved north-east for 30 min, distance = 40 x 0.5 = 20 miles

From trigonometry,

sin 45 = $\frac{y}{20}$ ; y = 20 sin 45 ; y= 14.14 miles

cos 45 = $\frac{x}{20}$ ; x = 20 cos 45 ; x = 14.14 miles

using Pythagoras theorem;

$z^{2}$ = $y^{2}$ + $(40+x)^{2}$

    = $14.14^{2}$ + $(40+14.14)^{2}$

     = 3131.08

$z^{2}$ = $\sqrt{3131.08}$

z = 55.96 miles