Linear equations word problems: tables - Questions

Answers

1. \(7.5\) degrees Celsius per minute.

Since the pizza was heated at a constant rate, the table describes a linear relationship.

Moreover, the rate of change of this relationship corresponds to the rate at which the pizza was heated.

The table of values shows that for each increase of \(6\) minutes in Time, Temperature increased by \(45\) degrees Celsius. The rate at which the pizza was heated is the ratio of those corresponding differences:

\(\frac{\Delta \text { Temperature }}{\Delta \text { Time }}=\frac{45}{6}=7.5\)

In conclusion, the pizza was heated at a rate of \(7.5\) degrees Celsius per minute.


2. \(14\) minutes.

Since the pizza was heated at a constant rate, the table describes a linear relationship.

Moreover, the time it took the pizza to reach \(100\) degrees Celsius corresponds to the case where the temperature was \(100\) degrees Celsius.

The table of values shows that for each increase of \(2\) minutes in the time, the temperature increased by \(15\) degrees celsius.

Time (minutes) Temperature (degrees Celsius)
\(4\) \(25\)
\(\stackrel{+2}{\longrightarrow} 6\) \(40 \stackrel{+15}{\longleftarrow}\)
\(\stackrel{+2}{\longrightarrow} 8\) \(55 \stackrel{+15}{\longleftarrow}\)


Let's extend the table to get to \(100\) degrees Celsius.

Time (minutes) Temperature (degrees Celsius)
\(8\) \(55\)
\(\stackrel{+2}{\longrightarrow} 10 \) \(70 \stackrel{+15}{\longleftarrow}\)
\(\stackrel{+2}{\longrightarrow} 12\) \(85 \stackrel{+15}{\longleftarrow}\)


In conclusion, the pizza reached \(100\) degrees Celsius after \(14\) minutes.


3. \(6\) minutes

Since Julia rode at a constant speed, the table describes a linear relationship.

Moreover, the rate of change of this relationship corresponds to the time it takes Julia to ride \(1\) kilometer.

The table of values shows that for each increase of \(2\) kilometers in Distance, Time increased by \(12\) minutes. The time it takes Julia to ride \(1\) kilometer is the ratio of those corresponding differences:

In conclusion, Julia rode \(1\) kilometer in \(6\) minutes.


4. \(10\) minutes

Since Julia rode at a constant speed, the table describes a linear relationship.

Moreover, the time it took Julia to get ready for the delivery corresponds to the case where the distance \(0\) kilometers.

The table of values shows that for each increase of \(2\) kilometers in the distance, the time increases by \(12\) minutes.

Distance (kilometers) Time (minutes)
\(6\) \(46\)
\(\stackrel{+2}{\longrightarrow} 8 \) \(58 \stackrel{+12}{\longleftarrow}\)
\(\stackrel{+2}{\longrightarrow} 10\) \(70 \stackrel{+12}{\longleftarrow}\)


Let's extend the table backwards to get to \(0\) kilometers.

Distance (kilometers) Time (minutes)
\(6\) \(46\)
\(\stackrel{-(2)}{\longrightarrow} 4\) \(34 \stackrel{-(12)}{\longleftarrow}\)
\(\stackrel{-(2)}{\longrightarrow} 2\) \(22 \stackrel{-(12)}{\longleftarrow}\)
\(\stackrel{-(2)}{\longrightarrow} 0\) \(10 \stackrel{-(12)}{\longleftarrow}\)


In conclusion, it took Julia \(10\) minutes to get ready for the delivery.