Question

guliskhan plans to cover a certain distance by running and bicycling. she runs at a constant speed, and she bicycles at a speed of 7 meters per second (m/s). let r represent the number of seconds that guliskhan runs and b represent the number of seconds that she bicycles according to her plan. 3r + 7b ≥ 1000 according to the inequality, at what speed does guliskhan run, and what is the minimum distance that she plans to cover? guliskhan runs at a speed of \boxed{} m/s, and plans to cover a minimum distance of \boxed{} meters. can guliskhan cover this minimum distance if she runs for 60 seconds and bicycles for 90 seconds? choose 1 answer: a yes b no

Explanation:

Step1: Determine running speed

The term \(3R\) in the inequality \(3R + 7B\geq1000\) represents the distance covered by running. Since distance = speed × time, and \(R\) is time in seconds, the speed for running is \(3\) m/s (because \(3\times R\) gives distance when \(R\) is time).

Step2: Determine minimum distance

The inequality \(3R + 7B\geq1000\) means the total distance (running distance + bicycling distance) is at least \(1000\) meters. So the minimum distance she plans to cover is \(1000\) meters.

Step3: Check if distance is covered

Substitute \(R = 60\) and \(B = 90\) into \(3R + 7B\). Calculate \(3\times60+7\times90 = 180 + 630 = 810\). Since \(810<1000\), she does not cover the minimum distance.

Answer:

Guliskhan runs at a speed of \(3\) m/s, and plans to cover a minimum distance of \(1000\) meters.
The answer to the yes/no question is B. No