Question

jim is riding his bike home from school. the school is 9 miles from his house and he rides his bike at a constant speed of 12 miles per hour. which of the following graphs best represents jim’s trip home? graphs w, x, and two others (partially visible) showing miles from home vs time (in minutes) with y-axis 0-9 and x-axis 0-90

Explanation:

Step1: Find time to reach home

First, we know that speed \( v = 12 \) miles per hour, distance \( d=9 \) miles. Using the formula \( t=\frac{d}{v} \), we convert the speed to miles per minute (since the graph is in minutes) or calculate time in hours and then convert to minutes.

\( t=\frac{9}{12}=\frac{3}{4} \) hours. To convert to minutes, multiply by 60: \( \frac{3}{4}\times60 = 45 \) minutes. So Jim should reach home in 45 minutes.

Step2: Analyze the graphs

• Graph W: The line reaches \( y = 0 \) (home) at \( x = 45 \) minutes. Let's check the slope (rate of change of distance with time). The initial distance is 9 miles, time to reach home is 45 minutes. The slope (speed in miles per minute) is \( \frac{9}{45}=0.2 \) miles per minute. Convert to miles per hour: \( 0.2\times60 = 12 \) mph, which matches the given speed.
• Graph X: Reaches home at 30 minutes. Speed would be \( \frac{9}{30}=0.3 \) miles per minute \( = 18 \) mph, which is not 12 mph.
• The other two graphs (assuming the bottom ones: one has a slower slope, taking more than 45 minutes, speed less than 12 mph; the last one is increasing, which doesn't make sense as distance from home should decrease).

So Graph W has the correct time (45 minutes) and correct speed (12 mph).

Answer:

The graph labeled W (the first graph on the top left) best represents Jim's trip home.