Question

lets consider what it means to travel at a constant speed of 58 miles per hour. imagine driving with your cruise - control turned on and the speedometer set at 58 miles per hour.
a. how far do you travel in

• 0.5 hours? 29 miles preview
• 2 hours? 116 miles preview
• 0.25 hour? 14.5 miles preview
• 3 hours? 174 miles preview
• 3.1 hours? 179.8 miles preview

b. when traveling at a constant speed of 58 miles per hour, a change in time of 0.25 hour will always result in a change in distance of 14.5 miles. preview
c. when traveling at a constant speed of 58 miles per hour, the ratio of a change in distance \\(\delta d\\) (in miles) and the corresponding change in time \\(\delta t\\) (in hours) is the constant value 58. we can also write \\(\frac{\delta d}{\delta t}=58\\).

• i. determine the value of \\(\frac{\delta d}{\delta t}\\) when \\(\delta d = 14.5\\) and \\(\delta t=\frac{1}{4}\\) preview
• ii. determine the value of \\(\frac{\delta d}{\delta t}\\) when \\(\delta d = 29\\) and \\(\delta t=\frac{1}{2}\\) 14.5 preview
• iii. determine the value of \\(\frac{\delta d}{\delta t}\\) when \\(\delta d = 116\\) and \\(\delta t = 2\\) 58 preview

d. determine if the following statement is true or false
true the ratio \\(\frac{\delta d}{\delta t}=58\\) says that the ratio of any change in distance (in miles) and its corresponding change in time (in hours) is 58 when traveling at a constant speed of 58 mph.

Explanation:

Step1: Recall speed - distance - time formula

$v=\frac{\Delta d}{\Delta t}$, so $\frac{\Delta d}{\Delta t}=v$.

Step2: Calculate for each case

i. $\frac{\Delta d}{\Delta t}=\frac{14.5}{\frac{1}{4}} = 58$.
ii. $\frac{\Delta d}{\Delta t}=\frac{29}{\frac{1}{2}} = 58$.
iii. $\frac{\Delta d}{\Delta t}=\frac{116}{2}=58$.

Answer:

i. 58
ii. 58
iii. 58
d. True