Lisa and Jill leave Jill's house at the same time. Lisa drives north and Jill drives west.

Question

Lisa's average speed is 12mph12⁢mph slower than Jill's. At the end of one hour, they are 6060 miles apart. Find Jill's average speed. (Round your answer to the nearest tenth.)

Answer 1

Let's say Lisa's speed is x and Jill's speed is x+12.  At any time t, Lisa will be xt miles north of Jill's house and Jill will be (x+12)t miles west of her own house.  These distances represent the two sides of a right triangle whose hypotenuse is the distance between the two girls at time t.  So use the Pythagorean Theorem.

 

a² + b² = c²                          c=60 miles

(xt)² + ((x+12)t)² = 60²               t=1 hour

x² + x² + 24x + 144 = 3600

2x² + 24x - 3456 = 0

2(x + 48)(x - 36) = 0

x = -48, 36

 

So Lisa's average speed is 36 mph and Jill's average speed is 48 mph.  (No rounding needed)