Carter left Town A at noon, driving toward Town B at an average speed of 50 mph. At 12:30 P.M., Max headed from Town B to Town A along the same road. At 3 P.M., they met each other along the way, and Carter realized that he had completed 60% of his journey.

A:How far was Town A from Town B?

B:At what speed was Max traveling?

So when they met, Carter had traveled for 3 hours and Max had traveled 2.5 hrs.

let Max's speed be x mph

Carter's distance = 150 miles
Max's distance = 2.5x

.60(150+2.5x) = 150
90 + 1.5x = 150
1.5x = 60
x = 40

a) distance between towns = 150 + 2.5(40)
= 250 miles

b) Max's speed is 40 mph

Thanks

A: To find the distance between Town A and Town B, we need to determine the time it took for Carter to cover 60% of his journey. Since Carter realized he had completed 60% at 3 P.M., and he started at noon, it means it took him 3 - 12 = 3 hours to cover 60% of the distance.

Let's denote the total distance between Town A and Town B as D. Carter covered 60% of D in 3 hours. Therefore, the remaining 40% of the distance would be covered in the same amount of time.

We can set up the equation:

Distance covered by Carter = 60% of D = 0.6D
Distance covered by Max = 40% of D = 0.4D

Since Carter traveled at an average speed of 50 mph, we can use the formula: distance = speed * time to find the distance covered by Carter in 3 hours:

0.6D = 50 * 3
0.6D = 150

Divide both sides of the equation by 0.6:
D = 150 / 0.6
D = 250

Therefore, Town A is 250 miles away from Town B.

B: Since Max covered the remaining 40% of the distance in the same amount of time as Carter, we can calculate his speed using the distance traveled and the time taken.

Distance covered by Max = 40% of D = 0.4D = 0.4 * 250 = 100 miles
Time taken = 3 hours

Therefore, Max's speed can be calculated using the formula: speed = distance / time:

Speed = 100 / 3 ≈ 33.33 mph

Hence, Max was traveling at approximately 33.33 mph.

To determine the distance between Town A and Town B, we first need to figure out Carter's journey time from noon to 3 P.M. Given that Carter was traveling at an average speed of 50 mph, we can calculate the duration of his journey by subtracting the starting and ending times:

3 P.M. - 12:00 P.M. = 3 hours

Since Carter realized that he had completed 60% of his journey by the time they met, we can determine that he had 40% of the journey left. To find the total journey time, we can divide 3 hours by 60%, which represents the portion Carter had completed:

3 hours / 0.6 = 5 hours

Now, we know that Max headed from Town B to Town A at 12:30 P.M., and they met at 3 P.M. This gives us a time interval of 2.5 hours. Since Max's journey took 2.5 hours, we can calculate his average speed by dividing the distance traveled (which is the same for both Carter and Max) by the time taken:

Speed = Distance / Time

To find the distance, we need to know that Max traveled for 2.5 hours at his average speed. Using the formula above, we substitute the given information:

Distance = Speed * Time
Distance = Speed * 2.5 hours

Since we previously established that Carter had traveled for 3 hours by the time they met, and he had completed 60% of the journey, we can calculate the total distance using his speed:

Distance = Speed * 3 hours

Since both Carter and Max traveled the same distance, we can equate the two equations:

Speed * 2.5 hours = Speed * 3 hours

Now we can isolate the speed variable:

2.5 hours = 3 hours

Speed = 50 mph

Therefore, both Carter and Max were traveling at an average speed of 50 mph.

To answer the first question, we need to know the distance Carter traveled in 3 hours.

Distance = Speed * Time
Distance = 50 mph * 3 hours
Distance = 150 miles

Thus, Town A is 150 miles away from Town B.