Chiamaka is 149 km from the university and drives 95 closer every hour. Valente is 170 km from the university and drives 110 km closer every hour. Let represent the time, in hours, since Chiamaka and Valente started driving toward the university. Complete the inequality to represent the times when Valente is closer than Chiamaka to the university.

Question

Chiamaka is 149 km from the university and drives 95 closer every hour. Valente is 170 km  from the university and drives 110 km closer every hour. Let     represent the time, in hours, since Chiamaka and Valente started driving toward the university. Complete the inequality to represent the times when Valente is closer than Chiamaka to the university.

Bytelearn · Accepted Answer

Define Time and Distances: Let's denote the time since Chiamaka and Valente started driving toward the university as t (in hours). We can write down the distances from the university for both Chiamaka and Valente as functions of time t. For Chiamaka: Distance from university after t hours = 149 - 95t. For Valente: Distance from university after t hours = 170 - 110t.Set Up Inequality: To find when Valente is closer to the university than Chiamaka, we need to find the values of t for which Valente's distance from the university is less than Chiamaka's distance from the university. So, we set up the inequality: 170 - 110t < 149 - 95tSolve for t: Now, we solve the inequality for t. First, we can add 110t to both sides to get all the t terms on one side: 170 - 110t + 110t < 149 - 95t + 110t This simplifies to: 170 < 149 + 15tIsolate t Term: Next, we subtract 149 from both sides to isolate the term with t: 170 - 149 < 149 - 149 + 15t This simplifies to: 21 < 15tDivide to Solve: Finally, we divide both sides by 15 to solve for t: 21 / 15 < 15t / 15 This simplifies to: t > 21 / 15We can simplify the fraction 21 / 15 by dividing both the numerator and the denominator by their greatest common divisor, which is 3: t > (21 / 3) / (15 / 3) t > 7 / 5 t > 1.4

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