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2 July, 02:04

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.

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  1. 2 July, 02:55
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    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
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