As part of a conditioning program, a jogger ran 12 mi in the same amount of time as it took a cyclist to ride 24 mi. the rate of the cyclist was 12 mph faster than the rate of the jogger. find the rate of the jogger and the rate of the cyclist.

Distance = time * speed

let x be rate of the cyclist

x-12 = the rate of the jogger

they have the same time

so:  12mi/(x-12)mph = 24mi / x mph

12x=24(x-12)

288=12x

x=24

rate of the cyclist =24 mph

rate of the jogger = 12 mph

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step-by-step explanation:

1+2+3+4+5+6+7+8+9+10 = 55

2*10 = 20

55-20 = 35