COT 3100 Quiz #1 (Version E): d = rt, logs, Random Algebra, Roots of Polynomials
2/14/2025
SOLUTIONS
Note: GUESS AND CHECK EARNS A MAX OF 2 out of 10 for ANY PROBLEM.
1) (10 pts) If Tom leaves for work at 7:50 am, driving at an average speed of 40 miles per hour, he
arrives at work 6 minutes late. If he leaves for work at the same time, but drives at an average of
60 miles per hour, he arrives at work 4 minute early.
(a) How far away is work from his house?
(b) What time is he supposed to arrive at work to be on time?
Let D be the distance, in miles, from Tom’s house to his work and let t, in hours, be the amount of
time he should take to drive to work to be on time. This givcs us the two equations:
𝐷 6 𝐷 4
= 𝑡 + 60 and 60 = 𝑡 − 60. Subtract the second equation from the first to yield:
40
𝐷 𝐷 6 4
− = − (− )
40 60 60 60
3𝐷 2𝐷 10
− =
120 120 60
1200
𝐷= = 20 𝑚𝑖𝑙𝑒𝑠
60
Now, let’s solve for t by plugging in this value of D into the first equation (second one works also):
20 6 1 1 4 4 60 𝑚𝑖𝑛
= 𝑡 + 60 →𝑡 = 2 − 10 = 10 ℎ𝑜𝑢𝑟𝑠 = 10 ℎ𝑟𝑠 × = 24 𝑚𝑖𝑛
40 1 ℎ𝑟
It follows that Tom is supposed to arrive at work at 8:14 am.
(a) 20 miles (b) 8:14 am
Grading: 2 pts for clearly setting up a variable or variables relevant to the problem
2 pts for setting up equations based on the given information
2 pts for solving the equations for at least one of the variables in the problem
2 pts for the answer to (a) based on the work.
2 pts for the answer to (b) based on the work.
This study source was downloaded by 100000897929959 from CourseHero.com on 04-12-2025 07:04:09 GMT -05:00
https://www.coursehero.com/file/248534081/Quiz1-VerE-25-02-14-Solpdf/
2/14/2025
SOLUTIONS
Note: GUESS AND CHECK EARNS A MAX OF 2 out of 10 for ANY PROBLEM.
1) (10 pts) If Tom leaves for work at 7:50 am, driving at an average speed of 40 miles per hour, he
arrives at work 6 minutes late. If he leaves for work at the same time, but drives at an average of
60 miles per hour, he arrives at work 4 minute early.
(a) How far away is work from his house?
(b) What time is he supposed to arrive at work to be on time?
Let D be the distance, in miles, from Tom’s house to his work and let t, in hours, be the amount of
time he should take to drive to work to be on time. This givcs us the two equations:
𝐷 6 𝐷 4
= 𝑡 + 60 and 60 = 𝑡 − 60. Subtract the second equation from the first to yield:
40
𝐷 𝐷 6 4
− = − (− )
40 60 60 60
3𝐷 2𝐷 10
− =
120 120 60
1200
𝐷= = 20 𝑚𝑖𝑙𝑒𝑠
60
Now, let’s solve for t by plugging in this value of D into the first equation (second one works also):
20 6 1 1 4 4 60 𝑚𝑖𝑛
= 𝑡 + 60 →𝑡 = 2 − 10 = 10 ℎ𝑜𝑢𝑟𝑠 = 10 ℎ𝑟𝑠 × = 24 𝑚𝑖𝑛
40 1 ℎ𝑟
It follows that Tom is supposed to arrive at work at 8:14 am.
(a) 20 miles (b) 8:14 am
Grading: 2 pts for clearly setting up a variable or variables relevant to the problem
2 pts for setting up equations based on the given information
2 pts for solving the equations for at least one of the variables in the problem
2 pts for the answer to (a) based on the work.
2 pts for the answer to (b) based on the work.
This study source was downloaded by 100000897929959 from CourseHero.com on 04-12-2025 07:04:09 GMT -05:00
https://www.coursehero.com/file/248534081/Quiz1-VerE-25-02-14-Solpdf/
