SOLUTION: Hi A teacher was driving at 40km per hour. One third of the way he ran out of petrol. If he ran the rest of the way at 10km per hour what was the average speed. Thanks

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Question 1184903: Hi
A teacher was driving at 40km per hour. One third of the way he ran out of petrol. If he ran the rest of the way at 10km per hour what was the average speed.
Thanks
Found 3 solutions by greenestamps, JBnovelwriter, josgarithmetic:
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the total distance.

He drove 1/3 of x at a rate of 40km/h; the time for doing that (distance divided by rate) was %28%281%2F3%29x%29%2F40.

He ran 2/3 of x at a rate of 10km/h; the time for doing that was %28%282%2F3%29x%29%2F10.

The total time is then



His average speed is the total distance, divided by the total time:

x%2F%283x%2F40%29+=+x%2840%2F%283x%29%29=40%2F3

ANSWER: His average speed was 40/3 km/h

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Here is an informal way of salving the problem -- much faster if you understand it... but not easy to understand.

He ran twice as far as he drove, at a rate 1/4 his driving speed.
That means he spent 2*4=8 times as much time running as driving.
His average speed was then

%288%2810%29%2B1%2840%29%29%2F9+=+120%2F9+=+40%2F3

Answer by JBnovelwriter(34) About Me  (Show Source):
You can put this solution on YOUR website!
[A teacher was driving at 40km per hour. One-third of the way he ran out of petrol. If he ran the rest of the way at 10km per hour what was the average speed.]
.
there's a flaw in this question. either you need a total distance or a total time to be able to solve this problem.
For example, if the total distance was 120km away that means he drove 1 hour and ran for 8 hrs for a total of 9hrs. so you would take 120km%2F9hr=13.3333km%2Fhr


Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
               SPEED        TIME       DISTANCE

DRIVING        40          d/(3*40)      d/3

RUNNING        10          2d/(3*10)     2d/3

Totals                    d/120+d/15      d

If you simplify the total time expression, this is 3d%2F40.

Question asked for the average speed (for the whole trip).
Distance Divided By Time:

d%2F%283d%2F40%29
d%2A%2840%2F%283d%29%29
%28d%2A40%29%2F%28d%2A3%29-------see the quantity distance d cancel as factor of 1.
40%2F3
highlight%2813%261%2F3%29 kilometers per hour