The Correct Answer and Explanation is:
Correct Answer: 60 mph
Explanation:
This problem can be solved by first determining the length of the bridge using the information provided about the lion, and then using that distance to calculate the cheetah’s speed.
The core formula for this calculation is Distance = Rate × Time.
First, we must find the length of the bridge. The lion’s speed is given in miles per hour (mph), but its crossing time is in seconds. To work with consistent units, we need to convert the lion’s speed to miles per second. There are 60 minutes in an hour and 60 seconds in a minute, so there are 3600 seconds in one hour. The lion’s speed is 45 miles per 3600 seconds.
Now, we can calculate the distance of the bridge:
Distance = Rate × Time
Distance = (45 miles / 3600 seconds) × 40 seconds
Distance = 1800 / 3600 miles
Distance = 0.5 miles
So, the bridge is half a mile long. Since the cheetah crosses the same bridge, we know it also travels 0.5 miles. We are given that the cheetah takes 30 seconds to do this.
Next, we calculate the cheetah’s speed using the same formula, rearranged as Rate = Distance / Time:
Cheetah’s Rate = 0.5 miles / 30 seconds
This gives us the speed in miles per second. To answer the question, we should convert this back to the more common unit of miles per hour. We do this by multiplying by the number of seconds in an hour:
Cheetah’s Rate (mph) = (0.5 miles / 30 seconds) × 3600 seconds/hour
Cheetah’s Rate (mph) = (0.5 × 3600) / 30
Cheetah’s Rate (mph) = 1800 / 30
Cheetah’s Rate (mph) = 60 mph
Alternatively, one could solve this using ratios. Since the distance is constant, speed and time are inversely proportional. The cheetah takes 30/40, or 3/4, of the time the lion takes. Therefore, its speed must be 4/3 of the lion’s speed. Calculating 45 mph × (4/3) also gives the final answer of 60 mph.
