contestada

Carmen rides her bicycle at a constant rate to the market. When she rides her bicycle back home along the same route, she bikes at three-quarters the rate she biked to the market. At any given time, t, the distance biked can be calculated using the formula d = rt, where d represents distance and r represents rate. If the trip home takes 12 minutes longer than the trip to the market, how many minutes does it take Carmen to bike home?

Respuesta :

1. let Carmen's average speed (her rate) be r when she goes from her house to the market

Carmen's rate when she comes back is 3/4r

2. let t be the time it takes Carmen to go from her house to the market

The same distance d, from house to market can be described with:

       (i)    [tex]d=rt[/tex]    (as she goes to the market)
and (ii)   [tex]d= \frac{3}{4} r(t+12)[/tex]    (as she comes back to her house)

so [tex]rt=\frac{3}{4} r(t+12)=\frac{3}{4} rt+\frac{3}{4} r*12=\frac{3}{4} rt+9r[/tex]
[tex]rt- \frac{3}{4}rt=9r [/tex]

[tex]\frac{1}{4}rt=9r[/tex]

[tex]\frac{1}{4}t=9[/tex]

t=36 (min), so t+12=48 min

answer: 48 min

Otras preguntas