What is the area of the trapezoid?
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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, , given as follows;
= The time Stanley spent swimming + The time Stanley spent running + The time Stanley spent biking
∴ = 1 + 1.5 + 3 = 5.5 hours.