Two stores were selling pumpkins on the first day of October. The first store had 190 pumpkins in stock when it opened and sold 10 pumpkins every hour. The other store had 164 pumpkins when it opened and sold 6 pumpkins every hour. The two stores opened at the same time.

Question

How many hours after opening did it take for the two stores to have the same number of pumpkins?
Simplify any fractions.
hours

Answer 1

Let's denote the number of hours after opening as \( h \).

For the first store, the number of pumpkins remaining after \( h \) hours can be expressed as: \[ \text{Pumpkins in Store 1} = 190 - 10h \]

For the second store, the number of pumpkins remaining after \( h \) hours is: \[ \text{Pumpkins in Store 2} = 164 - 6h \]

We need to find the point in time where both stores have the same number of pumpkins remaining: \[ 190 - 10h = 164 - 6h \]

Now, we'll solve this equation for \( h \). First, we can add \( 10h \) to both sides to eliminate \( h \) from the left side: \[ 190 = 164 + 4h \]

Next, subtract 164 from both sides: \[ 190 - 164 = 4h \] \[ 26 = 4h \]

Now, divide both sides by 4 to solve for \( h \): \[ h = \frac{26}{4} = \frac{13}{2} = 6.5 \]

Thus, it took 6.5 hours after opening for the two stores to have the same number of pumpkins.

The final answer is: \[ \boxed{6.5} \] hours.