Question

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?

Answer 1

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)
`d=rt` (as she goes to the market)
and (ii)
`d= (3)/(4) r(t+12)` (as she comes back to her house)

so
`rt=(3)/(4) r(t+12)=(3)/(4) rt+(3)/(4) r*12=(3)/(4) rt+9r`

`rt- (3)/(4)rt=9r`


`(1)/(4)rt=9r`


`(1)/(4)t=9`

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

answer: 48 min