Question

2.4 ps - 15
challenge a car is traveling at a steady speed. it travels 2\frac{1}{3} miles in 3\frac{1}{2} minutes. how far will it travel in 34 minutes? in 1 hour?
the car will travel \square miles in 34 minutes.
(simplify your answer. type an integer, proper fraction, or mixed number.)
enter your answer in the answer box and then click check answer.
1 part remaining

Explanation:

Step1: Convert mixed numbers to improper fractions

The distance traveled is \( 2\frac{1}{3} \) miles, which is \( \frac{2\times3 + 1}{3}=\frac{7}{3} \) miles. The time taken is \( 3\frac{1}{2} \) minutes, which is \( \frac{3\times2+ 1}{2}=\frac{7}{2} \) minutes.

Step2: Find the speed

Speed \( v=\frac{\text{distance}}{\text{time}} \), so \( v = \frac{\frac{7}{3}}{\frac{7}{2}} \). When dividing fractions, we multiply by the reciprocal: \( v=\frac{7}{3}\times\frac{2}{7}=\frac{2}{3} \) miles per minute.

Step3: Calculate distance in 34 minutes

Distance \( d = v\times t \), where \( t = 34 \) minutes. So \( d=\frac{2}{3}\times34=\frac{68}{3}=22\frac{2}{3} \) miles. Wait, wait, no, wait. Wait, the original problem: Wait, maybe I misread. Wait, the car travels \( 2\frac{1}{3} \) miles in \( 3\frac{1}{2} \) minutes. Let's re - do step 2.

Wait, \( 2\frac{1}{3}=\frac{7}{3} \), \( 3\frac{1}{2}=\frac{7}{2} \). Speed \( v=\frac{\frac{7}{3}}{\frac{7}{2}}=\frac{7}{3}\times\frac{2}{7}=\frac{2}{3} \) miles per minute. Then in 34 minutes, distance is \( \frac{2}{3}\times34=\frac{68}{3}=22\frac{2}{3} \)? Wait, no, wait, maybe the first part: Wait, the problem says "It travels \( 2\frac{1}{3} \) miles in \( 3\frac{1}{2} \) minutes. How far will it travel in 34 minutes?".

Wait, another way: Find how many times \( 3\frac{1}{2} \) minutes is in 34 minutes. \( 34\div3\frac{1}{2}=34\div\frac{7}{2}=34\times\frac{2}{7}=\frac{68}{7} \). Then multiply by the distance \( 2\frac{1}{3} \) miles. So \( 2\frac{1}{3}\times\frac{68}{7}=\frac{7}{3}\times\frac{68}{7}=\frac{68}{3}=22\frac{2}{3} \) miles. Yes, that's the same result.

Answer:

\( \frac{68}{3} \) (or \( 22\frac{2}{3} \))