Algebra 1- Need Help

Question

Kathy and Cheryl are walking in a fundraiser. Kathy completes the course in 2.5 hours and Cheryl completes the course in four hours. Kathy walks three miles per hour faster than Cheryl. Find Kathy’s speed and Cheryl’s speed.

Answer 1

Let Cheryl's speed be c; then, Kathy's speed is 3 mph faster, or c + 3

In 4 hours, Cheryl walks 4(c) = 4c;

In 2 1/2 hours, Kathy walks 2 1/2 (c+3) = 5/2c + 15/2

Then, they walk the same amount, so

4c = 5/2c + 15/2

3/2c = 15/2

c = 2/3 * 15/2 = 5

Cheryl's speed is 5 mph

Kathy's speed is 5+3 = 8 mph

As a check, 5 * 4 = 20; 8 * 2 1/2 = 20. They each travel 20 miles.

Answer 2

Start with the basic premise that distance = rate x time

Call Cheryl’s rate x. She walks for 4 hours so her distance is 4x

Kathy walks 3mph faster so her rate is (x+3). She walks for 2 1/2 hours so her distance is 2.5(x+3)

Since they both walk the same distance 4x= 2.5(x+3)

4x=2.5x+ 7.5

1.5x=7.5

x=7.5/1.5

x=5mph which is Cherry’s rate

Kathy’s rate is then 5+3 or 8mph