As a part of an exercise program, two students, Louisa and Alfredo, start walking each morning. They live 15 miles away from eac
h 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.
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
