if a barrier island that is 1 km wide and 10 km long loeses 1.5 m of its width per year to erosion by a longsore current, how long will the island take to lose one-fourth of its width?
375
To determine how long the island will take to lose one-fourth of its width, we can use the given information:
Width of the barrier island = 1 km
Length of the barrier island = 10 km
Rate of erosion per year = 1.5 m
First, we need to calculate the total width that the island needs to lose to decrease one-fourth of its original width:
One-fourth of the width = (1/4) x 1 km = 0.25 km
Now, we know that the rate of erosion is given per year and the width is given in kilometers. To have both values in the same unit, we should convert the width from kilometers to meters:
0.25 km = 0.25 x 1000 m = 250 m
Now, we can calculate the time it will take to lose one-fourth of the width by dividing the total width to be lost by the rate of erosion:
Time = Total width / Rate of erosion
Time = 250 m / 1.5 m/year
Dividing 250 m by 1.5 m/year, we find:
Time = 166.67 years
Therefore, the barrier island will take approximately 166.67 years to lose one-fourth of its width due to erosion.