Chiamaka is 149km from the university and drives 95km closer every hour. Valente is 170km from the university and drives 110km closer every hour. Let t 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. t select inequality symbol hours

Question

Chiamaka is  149km from the university and drives  95km closer every hour. Valente is  170km from the university and drives  110km closer every hour. Let  t 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.  t select inequality symbol hours

Bytelearn · Accepted Answer

Setting up distances: Let's set up the distances from the university for Chiamaka and Valente as functions of time, t. Chiamaka's distance from the university after t hours is: 149 - 95t. Valente's distance from the university after t hours is: 170 - 110t. We want to find when Valente is closer to the university than Chiamaka, which means Valente's distance is less than Chiamaka's distance. So, we set up the inequality: 170 - 110t < 149 - 95t.Solving the inequality: Now, we solve the inequality for t. First, we'll add 110t to both sides and add 149 to both sides to isolate the variable t. 170 - 110t + 110t < 149 - 95t + 110t 170 < 149 + 15tIsolating the variable t: Next, we subtract 149 from both sides to get the t term by itself. 170 - 149 < 15t 21 < 15tDividing both sides: Finally, we divide both sides by 15 to solve for t. 21/15 < t 1.4 < t

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