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 ->  Customizable Word Problem Solvers  -> Misc -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.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(52752) About Me  (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  t%5Bdrive%5D = %28%283%2F4%29%2Ad%29%2F50 = %283d%29%2F200 hours;


     the time to run    t%5Brun%5D = %28%281%2F4%29%2Ad%29%2F10 = d%2F40 hours.


V%5Baverage%5D = d%2F%28t%5Bdrive%5D%2Bt%5Brun%5D%29 = d%2F%28%28%283d%29%2F200%29+%2B+d%2F40%29%29 = 1%2F%283%2F200%2B1%2F40%29 = 1%2F%283%2F200+%2B+5%2F200%29 = 1%2F%28%288%2F200%29%29 = 200%2F8 = 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) About Me  (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

distance%2Frate+=+%28x%2F4%29%2F50+=+x%2F200

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

distance%2Frate+=+%283x%2F4%29%2F10+=+3x%2F40

The total time was

x%2F200%2B3x%2F40+=+x%2F200%2B15x%2F200+=+16x%2F200+=+x%2F12.5

His average speed in mph was

distance%2Ftime+=+x%2F%28x%2F12.5%29+=+12.5

(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

%28%2815%2A10%29%2B%281%2A50%29%29%2F16+=+200%2F16+=+12.5

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

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) About Me  (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 1%2F4 of the distance, and at 50 mph, time spent driving = 

With the student running 3%2F4 of the distance, and at 10 mph, time spent running = 

Average Speed = matrix%281%2C2%2C+Total%2C+distance%29%2Fmatrix%281%2C2%2C+Total%2C+Time%29

Average Speed = D%2F%28D%2F200+%2B+3D%2F40%29, with D being total distance