Question

Amanda and Jacob ran a relay race together. Amanda ran 200 meters at an average rate of 8 mps and then Jacob ran 294 meters at an average rate of 8.4 mps. In how many seconds did they complete the race?

a) 62.5 seconds
b) 66.6 seconds
c) 70.0 seconds
d) 73.4 seconds

Answer 1

Amanda and Jacob took a total of 60 seconds to complete the relay race, which is not listed among the provided options.

Step-by-step explanation:

To find out the total time Amanda and Jacob took to complete the race, we need to calculate the time each took to complete their respective parts of the race and then add those times together.

First, let's calculate Amanda's time. She ran 200 meters at a rate of 8 meters per second (mps).

We will use the formula for time, which is:

`\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]`

For Amanda:

`\[ \text{Time}_{\text{Amanda}} = \frac{200 \text{ meters}}{8 \text{ mps}} \]`

Dividing 200 meters by 8 mps gives:

`\[ \text{Time}_{\text{Amanda}} = 25 \text{ seconds} \]`

Now, we'll calculate Jacob's time. He ran 294 meters at a rate of 8.4 mps.

For Jacob:

`\[ \text{Time}_{\text{Jacob}} = \frac{294 \text{ meters}}{8.4 \text{ mps}} \]`

Dividing 294 meters by 8.4 mps gives:

`\[ \text{Time}_{\text{Jacob}} = 35 \text{ seconds} \]`

To find the total time taken, we add the time taken by Amanda and Jacob:

`\[ \text{Total time} = \text{Time}_{\text{Amanda}} + \text{Time}_{\text{Jacob}} \\\ \text{Total time} = 25 \text{ seconds} + 35 \text{ seconds} \\\text{Total time} = 60 \text{ seconds} \]`

So the total time taken for Amanda and Jacob to complete the race is 60 seconds, which is not among the provided options. Let's double-check our calculations.

For Amanda:

`\[ \text{Time}_{\text{Amanda}} = \frac{200 \text{ meters}}{8 \text{ mps}} = 25 \text{ seconds} \]`

For Jacob:

`\[ \text{Time}_{\text{Jacob}} = \frac{294 \text{ meters}}{8.4 \text{ mps}} \]`

When we calculate this without rounding, we get:

`\[ \text{Time}_{\text{Jacob}} = (294)/(8.4) = 35 \text{ seconds} \]`

Again, we add them together:

`\[ \text{Total time} = 25 \text{ seconds} + 35 \text{ seconds} = 60 \text{ seconds} \]`

The correct answer according to the calculations is 60 seconds. There seems to be no other logical answer based on the information given and the arithmetic performed.