A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast.

Question

A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast. If the car has maintained a constant speed of 56 mi/h, how far is it from its starting position? (Round your answer to one decimal place.)

Answer 1

1 hour east at 56 miles per hour means 56 miles east

then 30 minutes = 1/2 hour at 56 miles per hour means 56/2 = 28 miles North east

total distance east is 56 + 28/sqr2 = 56 + 19.8 = 75.8 miles

total distance north = 1/2 hour at 56 mph = 28/sqr2 = 19.8 miles

this creates a right trianlgle with sides 75.8 and 19.8. The hypotenuse is the distance from the starting point

d^2 = 75.8^2 + 19.8^2 = 5745, + 392 = 6137

d = sqr6137 = 78.3 miles from the starting point