cities A,B and B are equidistant from each other. A motorist travels from A to B at 30mi/h,from B TO C at 40mi/h ,and from C to A at 50mi/h.determine his average speed for the entire trip
As=total distance covered/time taken
As =total distan/time taken
To determine the average speed for the entire trip, we can use the formula:
Average Speed = Total Distance / Total Time
Let's first calculate the total distance for the entire trip. Since cities A, B, and C are equidistant from each other, we can assume that the distances between them are equal.
Let the distance between each city be represented by 'd'.
So, the total distance for the entire trip would be:
Total Distance = Distance AB + Distance BC + Distance CA
= d + d + d
= 3d
Now let's calculate the total time taken for the trip. We can use the formula:
Time = Distance / Speed
The time taken for each leg of the trip is as follows:
Time AB = Distance AB / Speed AB
= d / 30
Time BC = Distance BC / Speed BC
= d / 40
Time CA = Distance CA / Speed CA
= d / 50
The total time for the entire trip would be:
Total Time = Time AB + Time BC + Time CA
= (d / 30) + (d / 40) + (d / 50)
Now we have the total distance and the total time. Let's substitute these values into the formula to find the average speed:
Average Speed = Total Distance / Total Time
= 3d / [(d / 30) + (d / 40) + (d / 50)]
To simplify this equation, we can find a common denominator for the denominators in the Total Time:
Average Speed = 3d / [(5d + 4d + 3d) / (600d)]
= 3d / [12d / (600d)]
Simplifying further by canceling out the common factors of 'd':
Average Speed = 3 / [12 / 600]
= 3 / 0.02
= 150
Therefore, the average speed for the entire trip is 150 miles per hour.
To determine the average speed for the entire trip, we need to calculate the total distance traveled and the total time taken.
Given that cities A, B, and C are equidistant from each other, let's assume the distance between each city is 'd' miles.
To calculate the total distance, we need to find the distance traveled between A and B, B and C, and C and A.
Distance between A and B = d miles
Distance between B and C = d miles
Distance between C and A = d miles
Total distance traveled = (Distance between A and B) + (Distance between B and C) + (Distance between C and A)
= d + d + d
= 3d miles
Now, to find the total time taken for the trip, we need to calculate the time taken to travel between A and B, B and C, and C and A.
Time taken to travel from A to B = Distance / Speed
= d miles / 30 mi/h
= (1/30) hours per mile * d miles
= d/30 hours
Time taken to travel from B to C = Distance / Speed
= d miles / 40 mi/h
= (1/40) hours per mile * d miles
= d/40 hours
Time taken to travel from C to A = Distance / Speed
= d miles / 50 mi/h
= (1/50) hours per mile * d miles
= d/50 hours
Total time taken = (Time taken to travel from A to B) + (Time taken to travel from B to C) + (Time taken to travel from C to A)
= d/30 + d/40 + d/50
To calculate the average speed for the entire trip, we use the formula: Average Speed = Total Distance / Total Time
Average Speed = (Total Distance traveled) / (Total Time taken)
= (3d miles) / (d/30 + d/40 + d/50)
= (3d) / (d(1/30 + 1/40 + 1/50))
= (3) / (1/30 + 1/40 + 1/50)
Now, we can simplify the expression to find the average speed.