Question

Dan and Makiko started doing their homework at the same time. It took

Dan twice as long to finish his homework than Makiko did. If Dan also took
40 minutes longer than Makiko did, which of the following systems of
equations could be used to determine d, the amount of time Dan took to
finish his homework in minutes, and m, the amount of time it took Makiko
to finish her homework in minutes?
Choose 1 answer:

Answer 1

To represent the situation described, we can set up a system of equations using the variables d for Dan's time and m for Makiko's time:

1. Dan took twice as long as Makiko:

d = 2m

2. Dan also took 40 minutes longer than Makiko:

d = m + 40

So, the system of equations that can be used to determine d and m is:

1. d = 2m

2. d = m + 40

These equations capture the relationship between Dan's and Makiko's homework completion times as described in the problem.

Answer 2

`\begin{cases}d=2m\\m + 40 = d\end{cases}`

Explanation:

Let d be the amount of time Dan took to finish his homework (in minutes).

Let m be the amount of time Makiko took to finish her homework (in minutes).

We are told that it took Dan twice as long to finish his homework than Makiko did. This can be expressed as:

`d=2m`

We are told that Dan took 40 minutes longer than Makiko did. This can be expressed as:

`m + 40 = d`

Therefore, the system of equations that could be used to determine the amount of time Dan took to finish his homework (d) and the amount of time it took Makiko to finish her homework (m) is:

`\begin{cases}d=2m\\m + 40 = d\end{cases}`