~~ Phoebe spends 2 hours training for an upcoming race. She runs full speed at 8 miles per hour for the race distance; then she walks back to her starting point at 2 miles per hour. How long does she spend walking? How long does she spend running?

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Solution

$Let Phoebe spends time t_{1} hours running, then the distance covered by her while running = 8 \times t_{1} miles [Distance = speed \times time] Also, let she spends time t_{2} hours walking, then the distance covered by her while walking = 2 \times t_{2} miles [distance = speed \times time] Since, the distance covered while running will be equal to the distance covered while walking, therefore 2 \times t_{2} = 8 \times t_{1} \Rightarrow t_{2} = 4 \times t_{1} . . . . . . . . . . (1) [Dividing both sides by 2] Also, the total time spent in the training is 2 hours, then t_{1} + t_{2} = 2 Substituiting, t_{2} = 4 t_{1} from equation (1), we get t_{1} + 4 t_{1} = 2 \Rightarrow 5 t_{1} = 2 Dividing both sides by 5, we get t_{1} = \frac{2}{5} = 0.4 hours From equation (1), we get t_{2} = 4 \times t_{1} = 4 \times (0.4) = 1.6 hours Hence, the time spent running, t_{1} = 0.4 hours and the time spent walking, t_{2} = 1.6 hours .$

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