Arthur and Betty start walking toward each other when they are 122 m apart. Arthur has...
Arthur and Betty start walking toward each other when they are 122 m apart. Arthur has a speed of 2.7 m/s and Betty has a speed of 2.6 m/s. Their dog, Spot, starts by Arthur's side at the same time and runs back and forth between them at 6 m/s. By the time Arthur and Betty meet, what distance, in meter, has Spot run?
Homework Answers
Let's break down the scenario step by step to calculate the distance Spot has run:
Time taken for Arthur and Betty to meet: Let t be the time taken for Arthur and Betty to meet. We can use the formula for time, which is distance divided by speed. Distance = 122 m (they are 122 m apart initially) Speed of Arthur = 2.7 m/s Speed of Betty = 2.6 m/s
Since they are walking towards each other, their relative speed is the sum of their individual speeds. Relative speed = 2.7 m/s + 2.6 m/s = 5.3 m/s
Time taken (t) = Distance / Relative speed t = 122 m / 5.3 m/s ≈ 23.01 seconds
Distance Spot runs during this time: Since Spot is running back and forth between Arthur and Betty at 6 m/s, Spot's speed relative to Arthur and Betty is 6 m/s. Spot's speed relative to Arthur and Betty = 6 m/s
During the time t, Spot's total distance covered is the product of its speed and time. Distance covered by Spot = Spot's speed × time taken Distance covered by Spot = 6 m/s × 23.01 seconds ≈ 138.06 meters
Therefore, Spot has run approximately 138.06 meters by the time Arthur and Betty meet.
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