let the number of hours when the cost is the same by h hours
16h = 11h + 5
solve for h
16h = 11h + 5
solve for h
At Cora's Bike Shop, the total charge is $16 per hour for the bike and helmet rental. Therefore, the total charge at Cora's Bike Shop is 16x.
At Dave's Bike Shop, there is a charge of $11 per hour for the bike rental and a flat fee of $5 for the helmet rental. Thus, the total charge at Dave's Bike Shop is 11x + 5.
Setting up the equation to find the number of hours where the total charges are the same:
16x = 11x + 5
To solve for x, we need to isolate the variable x on one side of the equation. Subtracting 11x from both sides:
16x - 11x = 11x - 11x + 5
Simplifying:
5x = 5
Dividing both sides of the equation by 5:
5x/5 = 5/5
x = 1
Therefore, the total charges at both bike shops are the same after 1 hour.