find the expression

Question

Dinah rides her bike to and from school every day unless it rains. Let d be the distance in miles from Dinah’s home to school. Find two expressions that represent how far Dinah travels by bike in a 4-week period if there are 3 rainy days in week 1, 2 rainy days in week 2, and no rainy days for the remainder of the period.

Answer 1

So when there's no rain Dinah rides her bike 2 x d (to school, then back). 

Expression 1: Potential distance - rain-days 
4 weeks x 5 days/week x 2d/day = 40 d.   

then you subtract the days she didn't ride: 
    3 days in week 1 x 2d/day = 6 d  
    2 in week 2 x 2d = 4d   

Thus 40d- 6d - 4d = 30d. 

Expression 2: Add up days ridden 
week 1:  2 days x 2d/day = 4 
week 2: 3 days x 2d/day =   6 
week 3: 5 days x 2d/day = 10 
week 4: 5 days x 2d/day  = 10 
4 + 6 + 10 + 10 = 30d.