Question

Stanley practices his running, swimming and biking every day. During these practices he runs at 9 mph, bikes at 16 mph and swims at 2.5 mph. Yesterday he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?
(a) If Stanley swam for t hours yesterday, what was his running time?

(b) In terms of t, how long did Stanley bike yesterday?

(c) What distance did Stanley covered while swimming?

(d) What distance did Stanley covered while running?

(e) What distance did Stanley covered while biking?

(f) What was the total distance Stanley covered during practices in terms of t?

(g) Write the equation that will allow you to find the practice time.

(h) For how long did Stanley swim, run, and bike yesterday?

I understand if you don't know more than one, I just need you guys to answer at least one problem. I will of course be awarding brainiest, as well as a TON of points. This is dues tomorrow people, please help me.

Answer 1

Answer:

(a) Stanley's running time was 0.5 + t

(b) Stanley biked for = 1 + 2·t hours

(c) The distance Stanley covered while swimming = 2.5 miles

(d) The distance Stanley covered while running = 13.5 miles

(e) The distance Stanley covered while biking = 48 miles

(f) Total distance Stanley covered during practice in terms of t = 43.5·t + 20.5

(g) The equation for finding the practice time is 64 = 43.5·t + 20.5

(h) Stanley swam, ran and biked for a total time of 5.5 hours

Step-by-step explanation:

The speed with which Stanley runs = 9 mph

The speed with which Stanley bikes = 16 mph

The speed with which Stanley swims = 2.5 mph

The time Stanley (he) spent running = 30 minutes + The time he spent swimming

The time Stanley (he) spent biking  = 2 × The time The time (he) spent running

Let the time Stanley spent swimming = t in hours

(a) The time he spent running = 30 minutes + t = 0.5 + t

The time he spent running = 0.5 + t

Stanley's running time was 0.5 + t

(b) The time Stanley spent biking  = 2 × (30 minutes + t) = 2 × (0.5 + t)

The time Stanley spent biking  = 2 × (0.5 + t) = 1 + 2·t

The time Stanley spent biking  = 1 + 2·t

Stanley biked for = 1 + 2·t hours

Therefore, given that distance = Speed × Time, we have

t × 2.5 + 9×(0.5 + t) + 16 × (2 × (0.5 + t)) = 64

2.5·t + 4.5 + 9·S + 32·t + 16 = 64

43.5·t + 20.5 = 64

43.5·t = 64 - 20.5 = 43.5

43.5·t = 43.5

t = 43.5/43.5 = 1

t = 1 hour

The time Stanley spent swimming = t = 1 hour

The time he spent running = 0.5 + t = 0.5 + 1.5 = 1.5

The time Stanley spent running = 1.5 hours

The time Stanley spent biking  = 2 × (0.5 + t) = 2 × (0.5 + 1) = 2 × 1.5 = 3

The time Stanley spent biking  = 3 hours

(c) The distance Stanley covered while swimming = Stanley's swimming speed × The time Stanley spent swimming

∴ The distance Stanley covered while swimming = 2.5 mph × 1 hour = 2.5 miles

The distance Stanley covered while swimming = 2.5 miles

(d) The distance Stanley covered while running = Stanley's running speed × The time Stanley spent running

The distance Stanley covered while running = 9 mph × 1.5 hours = 13.5 miles

The distance Stanley covered while running = 13.5 miles

(e) The distance Stanley covered while biking = Stanley's biking speed × The time Stanley spent biking

The distance Stanley covered while biking = 16 mph × 3 hours =  48 miles

The distance Stanley covered while biking = 48 miles

(f) The total distance Stanley covered during practice in terms of t is given as follows;

Given that distance = Speed × Time, we have

Total distance = t × 2.5 + 9×(0.5 + t) + 16 × (2 × (0.5 + t))

Total distance =2.5·t + 4.5 + 9·S + 32·t + 16

Total distance Stanley covered during practice in terms of t = 43.5·t + 20.5

(g) The equation for finding the practice time is given as follows;

Total distance Stanley covered during practice = 64 = 43.5·t + 20.5

∴ The equation for finding the practice time is 64 = 43.5·t + 20.5

(h) Stanley swam, ran and biked for a total time, $t_{(tot)}$, given as follows;

$t_{(tot)}$ = The time Stanley spent swimming + The time Stanley spent running + The time Stanley spent biking

∴ $t_{(tot)}$ = 1 + 1.5 + 3 = 5.5 hours.