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Answer :
Final answer:
The meeting time for the runner and the cyclist is 3 hours because when we solve the equation (6 * t) + 27 = (15 * t), we find that 't' equals 3. Therefore, the correct answer is option b) 3 hours
Explanation:
The student is asking about the time it takes for a runner and a cyclist moving towards each other with given speeds to meet, assuming that the cyclist travels 27 more miles than the runner. To solve this, one can use the formula distance = speed × time. Let's denote the time it takes for them to meet as 't'.
We know the speed of the runner is 6 mph and the cyclist's speed is 15 mph. When they meet, the total distance covered will be the sum of the distances each has traveled. The equation based on the given information is:
(Speed of runner × time) + 27 miles = (Speed of cyclist × time)
Substituting the given speeds, we have:
(6 × t) + 27 = (15 × t)
By solving this equation, we find that 't' equals 3, which means the meeting time is 3 hours. Hence, the correct answer is option b) 3 hours.
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Rewritten by : Barada
It takes 3 hours for the runner and the cyclist to meet. The equation 15t = 6t + 27 is solved by simplifying and dividing both sides by 9, resulting in t = 3, which is choice b).
To solve the problem of how many hours it takes for a runner and a cyclist to meet when the cyclist has cycled 27 more miles than the runner has run, we must use the relationship between distance, speed, and time. The speed of the runner is given as 6 mph and the speed of the cyclist as 15 mph. We will let 't' represent the time in hours when they meet.
The distance the runner covers in time 't' is 6t miles, and the distance the cyclist covers is 15t miles. Since the cyclist has traveled 27 more miles than the runner, we can set up the equation:
15t = 6t + 27
By simplifying the equation, we get:
15t - 6t = 27
9t = 27
Dividing both sides by 9 gives us:
t = 27 / 9
t = 3
Therefore, it takes 3 hours for the runner and the cyclist to meet, which corresponds to answer choice (b).
