We appreciate your visit to John traveled from his house to Miami Florida in 6 hours going 14 mph faster than Elliot Elliot can drive from his house to Miami. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The distance from John's house to Miami, Florida is 420 miles, calculated by first determining John's speed using the given information and then applying the formula distance = speed times time.
To calculate the distance from John's house to Miami, Florida, we need to use the formula distance = speed times time. John's travel time is 6 hours. We are not directly given John's speed; instead, we know that Elliot drives 14 mph faster than John and it takes him 5 hours to cover the same distance. Let's denote John's speed as 's'. Therefore, Elliot's speed is 's + 14 mph'. Setting up an equation based on Elliot's travel information, we have distance = (s + 14 mph) times 5 hours.
Since they both travel the same distance, we can also write John's travel information as distance = s times 6 hours. Equating both expressions for distance, we get: s times 6 = (s + 14) times 5. Simplifying, we have 6s = 5s + 70, which leads to s = 70 mph. This means John's speed is 70 mph.
To find the distance to Miami, we return to the distance formula and substitute John's speed: distance = 70 mph times 6 hours = 420 miles. Hence, the distance from John's house to Miami, Florida is 420 miles.
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Answer:
420 miles
Step-by-step explanation:
Distance = rate × time
Let's say that the distance is D and that John's speed is S. We know that:
D = S × 6
When Elliot drives at speed S+14:
D = (S+14) × 5
Setting D = D:
S × 6 = (S+14) × 5
6S = 5S + 70
S = 70
Therefore, the distance D is:
D = 70 × 6
D = 420
The distance from John's house to Miami is 420 miles.
