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=?

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Birdie

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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 forT_{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 forT_{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 forT_{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).

Given:

Speed from A to B,

Speed from B to A,

Time from B to A,

Let's find the distance first.

Step 1: Convert the speed of B to A from m/min to km/h.

Step 2: Use the formula to find the distances.

Distance from A to B:

Distance from B to A:

Step 3: Set the distances equal since it is the same path.

Step 4: Substitute the formulas and solve for

Step 5: Solve for

Step 6: Solve for

Finally, let's find the distance from A to B using the previously calculated time.

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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