Solve the problem.
-A child on a swing sweeps out a distance of $20 \mathrm { ft }$ on the first pass. If she is allowed to continue swinging until she stops, and if on each pass she sweeps out a distance $\frac { 3 } { 4 }$ of the previous pass, how far does the child travel?
A) 60 ft
B) 100 ft
C) 80 ft
D) 40 ft

Question

Quizplus · Accepted Answer

The distance traveled by the child on each pass is 20 ft, $\frac{3}{4}$ of the previous pass.
So, the distances traveled by the child on the first few passes are:
Pass 1: 20 ft
Pass 2: $\frac{3}{4}$ of 20 ft = 15 ft
Pass 3: $\frac{3}{4}$ of 15 ft = $\frac{45}{4}$ ft
Pass 4: $\frac{3}{4}$ of $\frac{45}{4}$ ft = $\frac{135}{16}$ ft
And so on.

We need to find the total distance traveled by the child, which is the sum of distances traveled on all passes. This is an infinite geometric series with first term 20 ft and common ratio $\frac{3}{4}$. So, using the formula for the sum of an infinite geometric series, we get:

Total distance = $\frac{20}{1-\frac{3}{4}}$ = 80 ft

Therefore, the best choice is C) 80 ft.

Solve the Problem 20ft20 \mathrm { ft }20ft On the First Pass

Solve the Problem $20 \mathrm { ft }$ On the First Pass