Question

Driving from Tulsa to Detroit Dean averaged 50 mph. He figured that if he had average 60 mph he’s driving time will decrease three hours. How far is it from Tulsa to Detroit

Answer 1

Let \( d \) be the distance from Tulsa to Detroit in miles.

Using the relationship between distance, speed, and time, we can express the time it takes to travel the distance at different speeds.

1. When averaging 50 mph, the time \( t_1 \) taken is:
\[
t_1 = \frac{d}{50}
\]

2. When averaging 60 mph, the time \( t_2 \) taken is:
\[
t_2 = \frac{d}{60}
\]

According to the problem, if Dean had averaged 60 mph, his driving time would decrease by 3 hours:
\[
t_1 - t_2 = 3
\]

Substituting the expressions for \( t_1 \) and \( t_2 \):
\[
\frac{d}{50} - \frac{d}{60} = 3
\]

To solve this equation, first find a common denominator for the fractions, which is 300:
\[
\frac{6d}{300} - \frac{5d}{300} = 3
\]

Simplifying this gives:
\[
\frac{6d - 5d}{300} = 3
\]
\[
\frac{d}{300} = 3
\]

Now, multiply both sides by 300 to solve for \( d \):
\[
d = 3 \times 300 = 900
\]

Thus, the distance from Tulsa to Detroit is:
\[
\boxed{900} \text{ miles}
\]

To verify, we can check the times:
- At 50 mph: \( \frac{900}{50} = 18 \) hours.
- At 60 mph: \( \frac{900}{60} = 15 \) hours.

The difference in time is indeed \( 18 - 15 = 3 \) hours, confirming that the distance is correctly calculated.