Plz help me????? 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?
plz help i really need help
what you really need is to think about the problem.
By 12:30, car A had been traveling 1/2 hr at 50 mph. SO, it had gone 25 miles.
At 3:PM, both cars had been traveling an additional 2.5 hours, so Carter had gone another 2.5*50 = 125 miles.
Carter's total distance is thus 150 miles.
So, 150 is 60% of the distance.
150/.6 = 250 miles.
So, A is 250 miles from B.
Max took 2.5 hours to travel the other 100 miles, so he was going at 100/2.5 = 40 mph.
All you have to do to solve word problems is take each fact and write it as math.
A: To find the distance between Town A and Town B, we need to calculate the total distance Carter traveled before they met. Since Carter realized he had completed 60% of his journey at the time of the meeting, we can determine that the remaining distance for Carter was 40% of the total distance.
Let's assume the total distance between Town A and Town B is represented by 'D'. Therefore, the remaining distance for Carter is 0.4D.
Since Carter was traveling at an average speed of 50 mph, we can express his travel time as the remaining distance (0.4D) divided by his average speed (50 mph).
Carter's travel time = Remaining distance / Average speed = 0.4D / 50 mph.
Now, let's analyze Max's travel time. Max started his journey at 12:30 P.M. and met Carter at 3 P.M., meaning he traveled for 2.5 hours.
Max's travel time = 2.5 hours.
Since Max and Carter were traveling along the same road, the total travel time for both of them will be the same. So we can equate the two travel times:
Carter's travel time = Max's travel time.
0.4D / 50 mph = 2.5 hours.
To find the distance between Town A and Town B, we can rearrange the equation:
0.4D = 50 mph * 2.5 hours,
0.4D = 125,
D = 125 / 0.4,
D = 312.5 miles.
Therefore, Town A is 312.5 miles away from Town B.
B: Now let's find out Max's speed. Max traveled from Town B to Town A in 2.5 hours. We already know that the distance between the two towns is 312.5 miles, so we can calculate Max's speed by dividing the distance by the time taken:
Max's speed = Distance / Time = 312.5 miles / 2.5 hours,
Max's speed = 125 miles per hour.
Therefore, Max was traveling at a speed of 125 miles per hour.
To find the distance between Town A and Town B, we can first calculate the time it took for Carter to complete 60% of his journey.
Since Carter started driving from Town A at noon and they met at 3 P.M., he drove for a total of 3 hours.
Now, if Carter completed 60% of his journey in 3 hours, it means he had 40% of his journey remaining.
Since Carter's current speed is 50 mph, we can calculate his total journey time using the formula:
Total journey time = Distance / Speed
We can express the remaining 40% of the journey in terms of distance by using a ratio. Let's assume the total distance between Town A and Town B is D miles.
Remaining distance = 40% of D = 0.4 × D
Carter's remaining journey time = Remaining distance / Speed
= 0.4 × D / 50
Since Carter completed his journey in 3 hours, we can set up the equation:
Remaining journey time + 3 hours = Total journey time
0.4 × D / 50 + 3 = D / 50
Now, let's solve the equation for the distance D:
0.4 × D / 50 + 3 = D / 50
Multiplying both sides by 50:
0.4 × D + 150 = D
Subtracting 0.4 × D from both sides:
150 = 0.6 × D
Now, we can solve for D by dividing both sides by 0.6:
D = 150 / 0.6
D = 250
So, Town A is located 250 miles away from Town B.
Now, to find the speed at which Max was traveling, we know that he started traveling later at 12:30 P.M. and met Carter at 3 P.M., which means Max traveled for a total of 2.5 hours.
Since the distance between Town A and Town B is 250 miles, we can use the formula:
Speed = Distance / Time
Max's speed = 250 miles / 2.5 hours
Max's speed = 100 mph
Therefore, Max was traveling at 100 mph.