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). 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?

a. Speed: 3 m/s, Minimum distance: 700 m
b. Speed: 5 m/s, Minimum distance: 400 m
c. Speed: 7 m/s, Minimum distance: 300 m
d. Speed: 10 m/s, Minimum distance: 100 m

Answer 1

To find Guliskhan's running speed and the minimum distance she plans to cover, we solve the inequality 3r + 7b ≥ 1000. We find that her running speed is at least 317 m/s and the minimum distance she plans to cover is 700 m.

Step-by-step explanation:

To find the speed at which Guliskhan runs and the minimum distance she plans to cover, we need to solve the inequality 3r + 7b ≥ 1000.

Since Guliskhan runs at a constant speed, let's assume her running speed is r.

Let's solve the inequality:

3r + 7b ≥ 1000

Since b represents the speed of her cycling and it is given as 7 m/s, let's substitute it into the inequality:

3r + 7(7) ≥ 1000

Simplifying: 3r + 49 ≥ 1000

Subtracting 49 from both sides: 3r ≥ 951

Dividing by 3: r ≥ 317

So, the minimum speed at which Guliskhan runs is 317 m/s.

To find the minimum distance Guliskhan plans to cover, we can substitute the value of r into the inequality:

3(317) + 7b ≥ 1000

Simplifying: 951 + 7b ≥ 1000

Subtracting 951 from both sides: 7b ≥ 49

Dividing by 7: b ≥ 7

So, the minimum distance that Guliskhan plans to cover is 700 m.