Carter left town A at 8 a.m driving toward town B at an average speed of 60 mph. At 8:30 a.m, Mihn headed from town B to town A along the same road. At 11 a.m, they met each other along the way and Carter realized that he had completed 80% of his journey. A) How far was Town A from Town B? B)At what speed was Mihn traveling?
I got 500 miles for A)
C drives for 3 hours to meet M
M drives for 2.5 hours to meet C
Distance C = 60 * 3 = 180
Distance M = s(2.5) = 2.5 s
but we know 180 = .8 d
so
d = 225 (not 500)
distance M = .2 (225) = 45 miles
so s = 45/2.5 = 18 mph
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check
60 * 3 = 180
18 * 2.5 = 45
total miles = 180 + 45 = 225
.8 * 225 = 180
.2*225 = 45
Nikolai will teach, he is pro
To find the distance between Town A and Town B, we can use the concept of relative speed.
A) Let's first find the time it took for Carter to complete 80% of his journey. If he met Mihn at 11 a.m, it means he traveled for 3 hours (11 a.m - 8 a.m). Since he completed 80% of his journey in that time, we can calculate the total time to complete his journey using the equation:
Total time = Time for 80% / 0.8
Total time = 3 hours / 0.8 = 3.75 hours
Now, we can find the distance between Town A and Town B using the formula:
Distance = Speed x Time
Distance = 60 mph x 3.75 hours
Distance = 225 miles
Therefore, Town A is 225 miles away from Town B.
B) To find the speed at which Mihn was traveling, we need to determine the remaining distance that Mihn covered between 8:30 a.m and 11 a.m.
Since Carter completed 80% of the journey and met Mihn at 11 a.m, it means Mihn traveled the remaining 20% of the journey during the same time. We can calculate this distance using:
Remaining distance = Total distance - Distance covered by Carter
Remaining distance = 225 miles - (80% x 225 miles)
Remaining distance = 225 miles - 180 miles
Remaining distance = 45 miles
Therefore, Mihn traveled 45 miles from Town B to the meeting point (since they met halfway). As we know the time is 2.5 hours from 8:30 a.m to 11 a.m, we can calculate Mihn's speed using the formula:
Speed = Distance / Time
Speed = 45 miles / 2.5 hours
Speed = 18 mph
Therefore, Mihn was traveling at a speed of 18 mph.