5 Minute Math: Weighted Averages (not really) for distance, rate, time - Free Printable

Let's solve the problem step by step.

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Problem Summary:

- Two groups of hikers start 21 miles apart at 7:00 A.M.
- They are hiking toward each other.
- First group: Speed = 1.5 miles per hour
- Second group: Speed = 2 miles per hour
- Let $ t $ = time in hours they have been hiking

We are to complete the table using the formula:

$$
d = rt \quad \text{(distance = rate × time)}
$$

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Step 1: Complete the Table

We already have:

| Group | $ r $ (rate) | $ t $ (time) | $ d = rt $ (distance) |
|-------|----------------|----------------|--------------------------|
| First group of hikers | 1.5 | $ t $ | ? |
| Second group of hikers | 2 | $ t $ | ? |

Now calculate $ d = rt $ for each:

- First group:
$ d = 1.5 \times t = 1.5t $

- Second group:
$ d = 2 \times t = 2t $

So, the completed table is:

| Group | $ r $ | $ t $ | $ d = rt $ |
|-------|--------|--------|-------------|
| First group of hikers | 1.5 | $ t $ | $ 1.5t $ |
| Second group of hikers | 2 | $ t $ | $ 2t $ |

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Explanation:

- The first group travels $ 1.5t $ miles in $ t $ hours.
- The second group travels $ 2t $ miles in $ t $ hours.
- Since they are moving toward each other, the total distance covered together is:
$$
1.5t + 2t = 3.5t
$$
- They started 21 miles apart, so when they meet:
$$
3.5t = 21
$$
Solving for $ t $:
$$
t = \frac{21}{3.5} = 6 \text{ hours}
$$

So, they will meet after 6 hours, at 1:00 P.M.

But the question only asks to complete the table, which we have done.

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✔ Final Answer (Completed Table):

| Group | $ r $ | $ t $ | $ d = rt $ |
|-------|--------|--------|-------------|
| First group of hikers | 1.5 | $ t $ | $ 1.5t $ |
| Second group of hikers | 2 | $ t $ | $ 2t $ |

Let me know if you'd like to find when they meet or how far each has traveled!