Question

Kathy and Cheryl are walking in a fundraiser. Kathy completes the course in 4.8 hours and Cheryl completes the course in 8 hours. Kathy walks 2 miles per hour faster than Cheryl. Find kathy's Speed and cheryl's Speed.

Answer 1

Answer:

Kathy's speed is equal to $5\ mph$

Cheryl's speed is equal to $3\ mph$

Step-by-step explanation:

Let

x-----> Kathy's speed

y----> Cheryl's speed

d----> the distance in miles

t----> the time in hours

s-----> the speed in miles per hour

we know that

The speed is equal to the distance divided by the time

so

$s=d/t$

solve for the distance d

$d=st$

In this problem

$x=y+2$ ----> equation A

Kathy's speed

we have

$s=x\ mph$

$t=4.8\ h$

substitute in the formula of distance

$d=4.8x$ -----> equation B

substitute equation A in equation B

$d=4.8(y+2)$

$d=4.8y+9.6$ ------> equation C

Cheryl's speed

we have

$s=y\ mph$

$t=8\ h$

substitute in the formula of distance

$d=8y$ -----> equation D

Remember that the distance is the same in both cases

so

equate equation C and equation D and solve for y

$4.8y+9.6=8y$

$8y-4.8y=9.6$

$3.2y=9.6$

$y=3\ mph$

Find the value of x

$x=y+2$ -----> $x=3+2=5\ mph$