As a part of an exercise program, two students, louisa and alfredo, start walking each morning. they live 15 miles away from each other. they decide to meet one day by walking toward one another. after 2 hours they meet. if louisa walks one mile per hour faster than alfredo, find both of their walking speeds.

St=d
s=d/t
t=d/s

so we have several things:
distance of alfredo
speed of alfredo
time of alredo

distance of louisa
speed of louisa
time of louisa

we will represen them as follows

distance of alfredo=d1
speed of alfredo=s1
time of alredo=t1=2=t2

distance of louisa=d2
speed of louisa=s2
time of louisa=t2=2=t1

d=distance
t=time
total d=15 miles
t=2 hours
they both walk towards each other

louisa's speed is 1 mile per hour more than Alfredo so s2=s1+1

so we also have

d1+d2=15
s2=s1+1
t1=t2=2

we want to solve for s1 and s2
d=st
d1=(s1)(2)
 
d2=(s2)(2)
subsitute s1+1 for s2
d2=(s1+1)(2)
put back ino equation

(s1)(2)+(s1+1)(2)=15
distribute
2s1+2s1+2=15
2(s1)+2(s1)+2=15
add like terms
4(s1)+2=15
subtract 2 from both sides
4(s1)=13
divide both sides by 4
s1=13/4=3 and 1/4 mph

s2=s1+1
s2=3 and 1/4
s2=4 and 1/4 mph

check
d=st
t=2
alfredo's distance=(3 and 1/4) times 2=6 and 1/2
louisa's distance=(4 and 1/4) times 2=8 and 1/2
6 and 1/2+8 and 1/2=6+1/2+8+1/2=14+1=15

Alfredo's walking speed=3 and 1/4 miles per hour
Louisa's walking speed=4 and 1/4 miles per hour

aka
Alredospeed=3.25 mph
Louisaspeed=4.25 mph