\begin{tabular}{l} If Peter travel at $$ 100 \mathrm{~km} / \mathrm{h} $$ a journey takes 40 minutes. \ How long does the same joumey takes if he travel at $$ 80 \mathrm{~km} / \mathrm{h} $$ ? \ \hline \ \hline \ A. 100 minutes \ B. 50 minutes \ C. 32 minutes \ D. 60 minutes \ Decrease 90 in the ratio $$ 2: 3 $$\end{tabular}

Question

UpStudy AI · Accepted Answer

To solve the problem, we need to determine how long the journey takes when Peter travels at $$ 80 \, \text{km/h} $$ given that it takes $$ 40 $$ minutes at $$ 100 \, \text{km/h} $$.

### Step 1: Calculate the distance of the journey

First, we need to find the distance of the journey using the speed and time at $$ 100 \, \text{km/h} $$.

- Speed $$ v_1 = 100 \, \text{km/h} $$
- Time $$ t_1 = 40 \, \text{minutes} = \frac{40}{60} \, \text{hours} = \frac{2}{3} \, \text{hours} $$

Using the formula for distance:
$$
d = v \cdot t
$$
we can calculate the distance $$ d $$:
$$
d = 100 \, \text{km/h} \cdot \frac{2}{3} \, \text{hours} = \frac{200}{3} \, \text{km}
$$

### Step 2: Calculate the time taken at $$ 80 \, \text{km/h} $$

Now, we will find the time taken to cover the same distance $$ d $$ at $$ 80 \, \text{km/h} $$.

- Speed $$ v_2 = 80 \, \text{km/h} $$

Using the formula for time:
$$
t = \frac{d}{v}
$$
we can calculate the time $$ t_2 $$:
$$
t_2 = \frac{d}{v_2} = \frac{\frac{200}{3} \, \text{km}}{80 \, \text{km/h}} = \frac{200}{3 \cdot 80} \, \text{hours} = \frac{200}{240} \, \text{hours} = \frac{5}{6} \, \text{hours}
$$

### Step 3: Convert time to minutes

Now, we convert $$ t_2 $$ from hours to minutes:
$$
t_2 = \frac{5}{6} \, \text{hours} \cdot 60 \, \text{minutes/hour} = 50 \, \text{minutes}
$$

### Conclusion

The time taken for the journey at $$ 80 \, \text{km/h} $$ is $$ 50 $$ minutes.

Thus, the answer is **B. 50 minutes**.

### Additional Task: Decrease 90 in the ratio $$ 2:3 $$

To decrease $$ 90 $$ in the ratio $$ 2:3 $$, we first find the total parts of the ratio:
$$
2 + 3 = 5 \text{ parts}
$$

Now, we calculate the value of one part:
$$
\text{Value of one part} = \frac{90}{5} = 18
$$

Now, we decrease $$ 90 $$ by $$ 2 $$ parts:
$$
\text{Decrease} = 2 \cdot 18 = 36
$$

Finally, we subtract this decrease from $$ 90 $$:
$$
90 - 36 = 54
$$

So, decreasing $$ 90 $$ in the ratio $$ 2:3 $$ gives us $$ 54 $$.
The journey takes 50 minutes at 80 km/h.

If Peter travel at a journey takes 40 minutes.

How long does the same joumey takes if he travel at ?

A. 100 minutes

B. 50 minutes

C. 32 minutes

D. 60 minutes

Decrease 90 in the ratio

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Solución

Step 1: Calculate the distance of the journey

Step 2: Calculate the time taken at

Step 3: Convert time to minutes

Conclusion

Additional Task: Decrease 90 in the ratio

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If Peter travel at a journey takes 40 minutes. How long does the same joumey takes if he travel at ? A. 100 minutes B. 50 minutes C. 32 minutes D. 60 minutes Decrease 90 in the ratio