if a man travels r miles and hour for h hours and s miles an hour for t hours, what is his average rate in miles per hour for the ENTIRE distance traveled?
a. rh+st
b. r/h+s/t
c. rh+st/2
d. rh+st/h+t
is the answer b?
(r*h + s*t)/(h + t). = Average speed.
No, the average speed will be
totaldistance/totaltime
now, recall that distance=speed*time
Yes, the answer is b.
To find the average rate in miles per hour for the entire distance traveled, you need to consider the total distance traveled and the total time taken.
The man traveled r miles per hour for h hours and s miles per hour for t hours. Therefore, the total distance traveled is rh + st miles.
The total time taken is the sum of h and t hours.
To calculate the average rate, you need to divide the total distance traveled by the total time taken:
Average rate = Total distance / Total time
In this case, the average rate is (rh + st) / (h + t) miles per hour.
Therefore, the answer is b.
To find the average rate in miles per hour for the entire distance traveled, we need to calculate the total distance traveled and divide it by the total time taken.
Let's calculate the total distance traveled:
Distance traveled at r miles per hour for h hours = r * h
Distance traveled at s miles per hour for t hours = s * t
The total distance traveled is the sum of these distances,
Total Distance = r * h + s * t
Now, let's calculate the total time taken:
Time taken at r miles per hour for h hours = h
Time taken at s miles per hour for t hours = t
The total time taken is the sum of these times,
Total Time = h + t
Finally, to find the average rate in miles per hour for the entire distance traveled, we divide the total distance by the total time:
Average Rate = Total Distance / Total Time
Plugging in the values we calculated earlier,
Average Rate = (r * h + s * t) / (h + t)
Looking at the answer choices:
a. rh + st: This option does not divide the total distance by the total time, so it's incorrect.
b. r/h + s/t: This option correctly divides the total distance by the total time, so it could be the correct answer.
c. (rh + st)/2: This option divides the sum of the distances by 2 instead of dividing by the total time, so it's incorrect.
d. rh + st/h + t: This option adds the time values instead of dividing by them, so it's incorrect.
Therefore, the correct answer is b. r/h + s/t.