Question

Use table to answer the question
Time spent driving(hours). Distance traveled (miles)
0. 0
1/2. 30
1 1/2. 90
2. 120
4. 240
The table shows the distance traveled on a bus trip from Houston,tx to Dallas, tx as a function of time find the rate at which the bus is traveling
55 mph
60 mph
70 mph
65 mph

Answer 1

To find the rate at which the bus is traveling, we can calculate the speed by using the formula:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

Let's calculate the speed for some of the time intervals given in the table:

1. **From \(0\) to \(2\) hours:**
- Distance: \(120\) miles
- Time: \(2 - 0 = 2\) hours
\[
\text{Speed} = \frac{120 \text{ miles}}{2 \text{ hours}} = 60 \text{ mph}
\]

2. **From \(0\) to \(1/2\) hours:**
- Distance: \(30\) miles
- Time: \(1/2\) hours
\[
\text{Speed} = \frac{30 \text{ miles}}{0.5 \text{ hours}} = 60 \text{ mph}
\]

3. **From \(1/2\) to \(1.5\) hours:**
- Distance: \(90 - 30 = 60\) miles
- Time: \(1.5 - 0.5 = 1\) hour
\[
\text{Speed} = \frac{60 \text{ miles}}{1 \text{ hour}} = 60 \text{ mph}
\]

4. **From \(1.5\) to \(2\) hours:**
- Distance: \(120 - 90 = 30\) miles
- Time: \(2 - 1.5 = 0.5\) hours
\[
\text{Speed} = \frac{30 \text{ miles}}{0.5 \text{ hours}} = 60 \text{ mph}
\]

5. **From \(2\) to \(4\) hours:**
- Distance: \(240 - 120 = 120\) miles
- Time: \(4 - 2 = 2\) hours
\[
\text{Speed} = \frac{120 \text{ miles}}{2 \text{ hours}} = 60 \text{ mph}
\]

From all calculations, we can see that the bus is consistently traveling at 60 mph on this trip.

Thus, the answer is **60 mph**.