Question

A pilot keeps a log of her flight time and flight distance during an international flight, as shown in the table. The relationship is proportional.

Time (hours) 1
2
3
4
5

Distance (miles) 536
1,072
1,608
2,144
2,680


The co-pilot wants to calculate what time they passed a checkpoint at mile 1,500.
This can be determined using the equation _[blank 1]_ to find that they passed the checkpoint after approximately _[blank 2]_ hours.

Select two answers: one for blank 1 and one for blank 2. For blank 1, let t
be time in hours, and let d
be distance in miles.

Responses

blank 2: 2.80
blank 2: 2 point 8 0

blank 2: 0.36
blank 2: 0 point 3 6

blank 2: 2.36
blank 2: 2 point 3 6

blank 1: d=1,500t
blank 1: d is equal to 1 comma 500 t

blank 2: 1.40
blank 2: 1 point 4 0

blank 1: d=5361,500t
blank 1: d is equal to the fraction with numerator 536 and denominator 1 comma 500 t

blank 1: t=d536
blank 1: t is equal to d over 536

blank 1: t=536d

Answer 1

To find the time they passed the checkpoint at mile 1,500, we can use the relationship shown in the table. We can see that the relationship is proportional, which allows us to set up the equation based on the distance per hour.

Since we know 536 miles corresponds to 1 hour, we have:

\[
\text{Distance} = \text{Rate} \times \text{Time} \implies d = 536t
\]

To find the time \( t \) when \( d = 1500 \) miles, we rearrange the equation as follows:

\[
t = \frac{d}{536}
\]

Now, substituting \( d = 1500 \):

\[
t = \frac{1500}{536} \approx 2.80\ \text{hours}
\]

This means that the correct answers are:

**Blank 1:** \( t = \frac{d}{536} \) (or \( t\ is\ equal\ to\ d\ over\ 536 \))

**Blank 2:** 2.80 (or 2 point 8 0)

So the answers are:
- **Blank 1:** \( t = \frac{d}{536} \)
- **Blank 2:** 2.80