Question

PLEASE HELP 25 POINTS FOR YOU!

1)Sophie bikes s miles per hour. Her friend Rana is slower. Rana bikes r miles per hour.

a) Yesterday, Sophie biked for t hours. How many miles was Sophie's route?

b)Yesterday Rana biked m miles. How many hours did Rana bike yesterday?

c) Rana and Sophie went for a 20 mile bike ride today. Each girl biked at her usual speed. How long did Sophie wait for Rana at the end of the route?

d)Rana and Sophie each plan to bike 3 hours tomorrow . How much farther will Sophie bike than Rana

Answer 1

Answer: I got you!

Explanation:

a) Sophie's distance is given by the formula: distance = rate × time. Therefore, her distance yesterday is s × t miles.

b) Rana's time is given by the formula: time = distance ÷ rate. Therefore, her time yesterday is m ÷ r hours.

c) Sophie's time is given by the formula: time = distance ÷ rate. Let's call the time Sophie waits for Rana "w". Then we have two equations:

Sophie's distance: s × (w + t) = 20

Rana's distance: r × (w + t) = 20 - m

We can solve for "w" by substituting the second equation into the first equation:

s × (w + t) = 20 - r × (w + t) + m

(s + r) × (w + t) = 20 + m

w + t = (20 + m) ÷ (s + r)

w = (20 + m) ÷ (s + r) - t

Therefore, Sophie waits for Rana for (20 + m) ÷ (s + r) - t hours.

d) Sophie's distance tomorrow is s × 3 miles, and Rana's distance tomorrow is r × 3 miles. Therefore, the difference in distance is (s - r) × 3 miles.