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# From A to B, V=96km/h. From B to A, V=96km/h+200m/min and T=5 min less than A to B. distance from A to B=? time from A to B=?

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## Answer to a math question From A to B, V=96km/h. From B to A, V=96km/h+200m/min and T=5 min less than A to B. distance from A to B=? time from A to B=?

Birdie
4.5
To find the distance from A to B, we can use the formula:
\text{Distance} = \text{Speed} \times \text{Time}

Given:
Speed from A to B, V_{AB} = 96 \, \text{km/h}

Speed from B to A, V_{BA} = 96 \, \text{km/h} + 200 \, \text{m/min}

Time from B to A, T_{BA} = T_{AB} - 5 \, \text{min}

Let's find the distance first.

Step 1: Convert the speed of B to A from m/min to km/h.
V_{BA} = 96 \, \text{km/h} + \left$\frac{200}{1000}\right$ \times 60 \, \text{km/h} = 96 \, \text{km/h} + 12 \, \text{km/h} = 108 \, \text{km/h}

Step 2: Use the formula to find the distances.
Distance from A to B:
\text{Distance}_{AB} = V_{AB} \times T_{AB}

Distance from B to A:
\text{Distance}_{BA} = V_{BA} \times T_{BA}

Step 3: Set the distances equal since it is the same path.
\text{Distance}_{AB} = \text{Distance}_{BA}

Step 4: Substitute the formulas and solve for T_{AB} .
V_{AB} \times T_{AB} = V_{BA} \times T_{BA}

96 \, \text{km/h} \times T_{AB} = 108 \, \text{km/h} \times $T_{AB} - 5 \, \text{min}$

Step 5: Solve for T_{AB} .
96\,\text{km/h}\times T_{AB}=108\,\text{km/h}\times T_{AB}-9\,\text{km}

108\,\text{km/h}\times T_{AB}-96\,\text{km/h}\times T_{AB}=9\,\text{km}

12\,\text{km/h}\times T_{AB}=9\,\text{km}

Step 6: Solve for T_{AB} .
T_{AB}=\frac{9\,\text{km}}{12\,\text{km/h}}=\frac{3}{4}\,\text{hours}

Finally, let's find the distance from A to B using the previously calculated time.
\text{Distance}_{AB}=96\,\text{km/h}\times\frac{3}{4}\,\text{hours}=\boxed{72\,\text{km}}

Answer: The distance from A to B is 72 km and the time from A to B is 3/4 hours $or 45 minutes$.

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