SOLUTION: Hi a student was driving to school at 50mph. A quarter of the way he ran out of petrol. If he ran the rest of the way at 10mph what was his average speed. thank you

Algebra.Com
Question 1149780: Hi
a student was driving to school at 50mph. A quarter of the way he ran out of petrol. If he ran the rest of the way at 10mph what was his average speed.
thank you
Found 3 solutions by ikleyn, greenestamps, MathTherapy:
Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
.
a student was driving to school at 50mph. A quarter of the way he ran out of petrol.
If he ran the rest of the way at 10mph what was his average speed.
~~~~~~~~~~~~~~~~~ 


Let " d " be the full distance.


Then the time to drive   =  =  hours;


     the time to run     =  =  hours.


 =  =  =  =  =  =  = 25 miles per hour.    ANSWER

Solved.

===============

After reading the note from @greenestamps: 

    dear greenestamps, you are not right (!!)


    The problem says it directly and explicitly :  " . . .  A quarter of the way  he ran out of petrol."

    Not a quarter of the time . . .

My solution is correct (!)


Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


(1) An elementary school solution method: choose a number for the distance to school so you have actual numbers to work with, and perform the actual calculations.

Although it makes the real world situation absurd, choose a distance that makes the numbers you have to work with "nice". Since he drove at 50mph for one-quarter of the distance, let the distance be 200 miles.

Then he drove 50 miles at 50mph and ran 150 miles at 10mph. That's 50/50 = 1 hour driving and 150/10 = 15 hours running, a total of 16 hours.

And 200 miles in 16 hours is an average of 200/16 = 12.5 mph.

(2) A solution using not-so-basic algebra: let the distance be x and solve an equation.

He drove 1/4 of the distance x at 50 mph; the time required in hours was



He ran 3/4 of the distance x at 10 mph; the time required in hours was



The total time was



His average speed in mph was



(3) A more advanced solution method, using logical reasoning instead of formal algebra....

Comparing his driving and his running, he ran 3 times as far as he drove at a rate 1/5 as fast; that means he spent 3*5=15 times as long running as driving. So his average speed in mph was



--------------------------------------------------------

For tutor @ikleyn....

Oops!!

He drove for 1/4 of the time and ran for 3/4 of the time....

--------------------------------------------------------

After reading tutor @ikleyn's response to my comment to her....

Yes, I stated my comment to her incorrectly; the problem says he drove 1/4 of the DISTANCE and ran for 3/4 of the DISTANCE.

But while my comment was written incorrectly, my solutions (by three different methods) worked the problem correctly, showing him driving for 1/4 of the distance and running for 3/4 of the distance.

My solutions were right.

Tutor @ikleyn's solution is wrong, having him driving for 3/4 of the distance and running for 1/4 of the distance -- contrary to the statement of the problem.
Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!
Hi
a student was driving to school at 50mph. A quarter of the way he ran out of petrol. If he ran the rest of the way at 10mph what was his average speed.
thank you
With the student driving  of the distance, and at 50 mph, time spent driving = 

With the student running  of the distance, and at 10 mph, time spent running = 

Average Speed = 

Average Speed = , with D being total distance

 

RELATED QUESTIONS


Hi
A teacher was driving at 40km per hour. One third of the way he ran out of petrol. If  (answered by greenestamps,JBnovelwriter,josgarithmetic)

Hi
Sally walked halfway to school at 5km per hour. She then ran the rest of the way at... (answered by greenestamps,ikleyn,robertb)

Bronson roared off on his motorcycle at 60 mph.  Then, much to his chagrin, he ran out of  (answered by checkley77)

Tom's home is 1,800 m from his school. One morning he walked part of the way to school... (answered by josmiceli)

Tom's home is 1,800 m from his school. One morning he walked part of the way to school... (answered by lwsshak3)

Tom's home is 1,800 m from his school. One morning he walked part of the way to school... (answered by lwsshak3)

Joe ran up a path to the top of a hill at an average speed of 2 mph and ran down the same  (answered by checkley77)

Justin recently drove to see his parents who live 390 miles away. on his way there his... (answered by CharlesG2)

Justin recently drove to visit his parents who live 100 miles away. On his way there his... (answered by stanbon)