Question

Kelly drove north for 9 miles and then east for 12 miles at an average rate of 42 miles per hour to arrive at the town of Prime. Brenda left from the same location, at the same time, and drove along a straight road to Prime at an average rate of 45 miles per hour. How many minutes earlier than Kelly did Brenda arrive?

Answer 1

Answer:

Step-by-step explanation:

This is one of the more interesting motion problems I've seen.  I like it!  If Kelly is driving north (straight up) for 9 miles, then turns east (right) and drives for 12 miles, what we have there are 2 sides of a right triangle.  The hypotenuse is created by Brenda's trip, which originated from the same starting point as Kelly and went straight to the destination, no turns.  We need the distance formula to solve this problem, so that means we need to find the distance that Brenda drove.  Using Pythagorean's Theorem:

$9^2+12^2=c^2$ and

$81+144=c^2$ and

$225=c^2$ so

c = 15.

Brenda drove 15 miles.  Now we can fill in a table with the info:

                d        =        r        x        t

Kelly     12+9               42                t

Brenda    15                45                t

Because they both left at the same time, t represents that same time, whatever that time is.  That's our unknown.

If d = rt, then for Kelly:

21 = 42t

For Brenda

15 = 45t

Solve Kelly's equation for t to get

t = 1/2 hr or 30 minutes

Solve Brenda's equations for t to get

t = 1/3 hr or 20 minutes

That means that Brenda arrived at the destination 10 minutes sooner than Kelly.