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Assume the distance from San Francisco to Big Sur California is 240 kilometers. Han Fei leaves Big Sur on her bicycle heading for San Francisco at 20 kilometers per hour; at the same time Mohammed leaves San Francisco in his car heading to Big Sur on the same route averaging 40 miles per hour. How far from San Francisco will Han Fei be when Mohammed meets her in his car?

User CJ Hanson
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2 Answers

3 votes

Final answer:

To solve the relative motion problem, Mohammed's speed is converted to kilometers per hour, and the combined speed is used to find the meeting time. Multiplying Han Fei's cycling speed by this time results in a meeting point of approximately 56.86 kilometers from San Francisco.

Step-by-step explanation:

The question involves a relative motion problem where two individuals are moving toward each other from opposite ends of a route with different speeds. Han Fei leaves Big Sur on her bicycle heading toward San Francisco at 20 kilometers per hour, while Mohammed leaves San Francisco in his car heading to Big Sur at 40 miles per hour. We need to determine the point at which they meet, specifically how far from San Francisco they encounter each other.

First, we need to convert Mohammed's speed to kilometers per hour since the question provides distances in kilometers. There are approximately 1.60934 kilometers in a mile, so 40 miles per hour is equivalent to 40 * 1.60934 = 64.3736 kilometers per hour.

Now that the speeds are in the same units, we can calculate how long it will take for Mohammed and Han Fei to meet. Since they start at the same time and move towards each other, they are closing the distance between them at a rate of the sum of their speeds. This rate is 20 km/h + 64.3736 km/h = 84.3736 km/h.

The distance between San Francisco and Big Sur is 240 kilometers. To find the time it will take for them to meet, divide the distance by the combined speed: 240 km / 84.3736 km/h = 2.843 hours (approximately).

To find out how far from San Francisco Han Fei will be when they meet, multiply Han Fei's speed by this time: 20 km/h * 2.843 hours = 56.86 kilometers (approximately). So Han Fei will be approximately 56.86 kilometers from San Francisco when Mohammed meets her.

User GONeale
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5 votes

Answer: When Mohammed meets Han Fei, she will be 74.6 kilometers away from San Francisco.

Step-by-step explanation:

First, we need to convert Mohammed's speed from miles per hour to kilometers per hour, as Han Fei's speed is given in kilometers per hour.


40 miles per hour = 64.37 kilometers per hour (approximately)

Now, let's determine how long it will take Mohammed to reach the point where he meets Han Fei:

time = distance ÷ speed

time = 240 km ÷ 64.37 km/h

time ≈ 3.73 hours

So, after 3.73 hours, Mohammed will meet Han Fei.

In that time, Han Fei will have traveled:

distance = speed × time

distance = 20 km/h × 3.73 h

distance ≈ 74.6 km

User Elpezmuerto
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