Find the unit rate

Question

Brynn is mowing the lawn. If it has taken 1/2
hour to mow 2/3
of the lawn, how long will it take to mow the entire lawn?

(1 point)
Responses

16
of an hour
1 sixth of an hour

34
of an hour
3 fourths of an hour

13
of an hour
1 third of an hour

1 1/3
hours

Answer 1

To find the unit rate, we need to determine how long it takes Brynn to mow the entire lawn based on the work done so far.

1. Calculate the rate at which Brynn mows the lawn:

   • Brynn has mowed \( \frac{2}{3} \) of the lawn in \( \frac{1}{2} \) hour.

2. Find the time it takes to mow the entire lawn:

   • We can set up a proportion to find out how long it takes to mow \( 1 \) whole lawn:
   • If mowing \( \frac{2}{3} \) of the lawn takes \( \frac{1}{2} \) hour, then mowing \( 1 \) whole lawn (let's call that \( x \) hours) would satisfy: \[ \frac{2}{3} \text{ lawn} \rightarrow \frac{1}{2} \text{ hour} \] \[ 1 \text{ lawn} \rightarrow x \text{ hours} \]

   The proportion can be set up as: \[ \frac{\frac{2}{3}}{1} = \frac{\frac{1}{2}}{x} \]

3. Cross-multiply to solve for \( x \): \[ \frac{2}{3} x = \frac{1}{2} \] Multiply both sides by \( \frac{3}{2} \) to isolate \( x \): \[ x = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \]

This means it will take Brynn \( \frac{3}{4} \) of an hour to mow the entire lawn.

Thus, the answer is 3 fourths of an hour.