A car travels downhill at 72 mph (miles per hour), on the level at 63 mph, and uphill at only 56 mph The car takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes.

  1. 273 miles

  2. 723 miles

  3. 434 miles

  4. none of these


Correct Option: A

AI Explanation

To solve this question, let's calculate the distance between town A and town B.

Let's assume the distance between town A and town B is "d" miles.

On the first trip, the car travels downhill at 72 mph for a certain distance, on the level at 63 mph for a certain distance, and uphill at 56 mph for the remaining distance.

The total time taken for the first trip is 4 hours.

Using the formula distance = speed × time, we can write the equation:

(distance downhill / 72) + (distance level / 63) + (distance uphill / 56) = 4

On the second trip, the car takes 4 hours and 40 minutes, which is equivalent to 4 + 40/60 = 4.67 hours.

Using the same formula, we can write the equation:

(distance downhill / 72) + (distance level / 63) + (distance uphill / 56) = 4.67

Now, let's solve these equations to find the distance "d."

To make the calculations easier, let's multiply both equations by the least common multiple (LCM) of the denominators (72, 63, and 56), which is 2268.

2268 * (distance downhill / 72) + 2268 * (distance level / 63) + 2268 * (distance uphill / 56) = 2268 * 4 2268 * (distance downhill / 72) + 2268 * (distance level / 63) + 2268 * (distance uphill / 56) = 2268 * 4.67

Canceling out the denominators, we get:

31 * distance downhill + 36 * distance level + 40.5 * distance uphill = 9072 31 * distance downhill + 36 * distance level + 40.5 * distance uphill = 10508.76

Now, let's solve these equations simultaneously to find the distances traveled downhill, on the level, and uphill.

By subtracting the first equation from the second equation, we get:

40.5 * distance uphill - 40.5 * distance uphill = 10508.76 - 9072 0 = 1436.76

This equation is not possible, as it implies 0 = 1436.76, which is false.

Therefore, none of the given options (A, B, C, or D) is correct.

Please check the question or provide additional information if necessary.

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