Question

Mateo has already swum Four-fifths of the 2,000 meters he is swimming today. If he continues swimming at a pace of Three-fourths of a meter per second, which expression shows the amount of time it will take him to swim the remaining distance?
2000 times four-fifths times three-fourths
2000 times four-fifths divided by three-fourths
2000 times one-fifth times three-fourths
2000 times one-fifth divided by three-fourths

Answer 1

To determine the time it will take Mateo to swim the remaining distance, we first need to find out how much distance he has left to swim.

1. Calculate the distance he has already swum:
\[
\text{Distance swum} = 2000 \times \frac{4}{5} = 1600 \text{ meters}
\]

2. Calculate the remaining distance:
\[
\text{Remaining distance} = 2000 - 1600 = 400 \text{ meters}
\]

3. Mateo is swimming at a pace of \(\frac{3}{4}\) meters per second. To find the time \(t\) it will take him to swim the remaining 400 meters, we use the formula:
\[
t = \frac{\text{distance}}{\text{speed}} = \frac{400}{\frac{3}{4}}
\]

To simplify \(\frac{400}{\frac{3}{4}}\), we multiply by the reciprocal:
\[
t = 400 \times \frac{4}{3} = \frac{1600}{3} \text{ seconds}
\]

Now we can express the remaining distance he needs to swim in terms of the original question's options.

The correct expression to represent the time it takes Mateo to swim the remaining distance is:
\[
\frac{2000 \times \frac{1}{5}}{\frac{3}{4}}
\]
because:

- The remaining distance is \(\frac{2000 \times 1}{5}\) (since \(\text{remaining distance} = 400 = 2000 \times \frac{1}{5}\)).
- You then divide by his speed \(\frac{3}{4}\) to find the time.

So, the correct option is:
**2000 times one-fifth divided by three-fourths.**