SOLUTION: Hi Sally walked halfway to school at 5km per hour. She then ran the rest of the way at 8km per hour. If she rode home at a speed of 40km per hour,what was her average speed to and

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Question 1183834: Hi
Sally walked halfway to school at 5km per hour. She then ran the rest of the way at 8km per hour. If she rode home at a speed of 40km per hour,what was her average speed to and from school.
Thanks
Found 3 solutions by greenestamps, ikleyn, robertb:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


This kind of problem is probably easiest to solve if we choose a "nice" number for the distance to the school. Since the given speeds are 5, 8, and 40km/h, we can choose 40km for the distance to the school. Note that choice is not reasonable in the real situation -- but it makes solving the problem easy.

She walks half of the 40km at 5km/h, taking 20/5 = 4 hours.
She walks half of the 40km at 8km/h, taking 20/8 = 2.5 hours.
She rides back the whole 40km at 40km/h, taking 40/40 = 1 hour.

In all, she traveled 80km in 4+2.5+1 = 7.5 hours; her average speed was 80/7.5 = 160/15 = 32/3km/hr or 10 2/3 km/h.

ANSWER: 10 2/3 km/hr

If you need to solve the problem using formal algebra, simply use d for the distance instead of choosing a specific number. Then the total time for the trip is



and her average speed was the total distance divided by the total time:

2d%2F%283d%2F16%29+=+2d%2816%2F3d%29+=+32%2F3

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.


            I will show you absolutely unexpected way to solve the problem
            (which you did not expect to see). 


For the way to school (consisting of two equal parts), you can calculate the average speed on this part 
of the traveled distance using the formula


      v = %282%2A5%2A8%29%2F%285%2B8%29 = 80%2F13  km/h.


Now you have two other equal parts: the way to there and the way back.


These ways are of the same length, so you can apply similar formula for the entire trip to school and back


     w = %282%2A%2880%2F13%29%2A40%29%2F%2880%2F13%2B40%29.


I leave calculations to you.


As the answer, you should get the same number as other tutors produced in their posts.


Regarding the formula, see my post at the link
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1183833.html


See also the lessons
    - Calculating an average speed: a train going from A to B and back
    - One more problem on calculating an average speed
in this site.



Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = distance from home to school
===> 2d = total distance travelled to and from school
===> %28d%2F2%29%2F5+=+d%2F10 = time in the walking part of the trip
===>%28d%2F2%29%2F8+=+d%2F16 = time in the running part of the trip
===> d%2F40 = time in the riding part, going back home.
===> Average speed to and from school = Total distance/Total time of travel
= kph