SOLUTION: Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a speed of 12 mph. What was his speed for the remaini

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Question 1019106: Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a speed of 12 mph. What was his speed for the remaining distance? What was his average speed?
Found 3 solutions by jorel555, MathTherapy, ikleyn:
Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
The first mile is at 12 mph, which would take 5 minutes to finish. The second mile takes 10 minutes, which is 60/10, or 6 mph. The average for the two miles is 12+6/2, or 9 mph!!!!!!!!!!!!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a speed of 12 mph. What was his speed for the remaining distance? What was his average speed?
Speed for 2nd leg: highlight_green%28matrix%281%2C2%2C+6%2C+mph%29%29

Average speed: 2%2F%2815%2F60%29, or highlight_green%28matrix%281%2C2%2C+8%2C+mph%29%29

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance
he biked at a speed of 12 mph. What was his speed for the remaining distance? What was his average speed?
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"the first half of the distance he biked at a speed of 12 mph".
So, Ling biked 1 miles at the speed of 12 mph = 12%2F60 = 0.2 miles per minute. 
Thus Ling spent 1%2F0.2 = 5 minute to cover the first half of the distance.

For the second half, which is also 1 mile, Ling spent the remaining 15-5 = 10 minutes, i.e. twice the time he spent for the first mile. 
It means that his speed was half of the speed on the first mile, 12%2F2 = 6 mph.

It is the answer to the first question.

Regarding the average speed, it is the FULL distance divided by the FULL time, i.e. v%5Baver%5D = 2%2F%28%281%2F4%29%29 = 2*4 = 8 mph. 
(Here 1%2F4 is 15 minutes = 1/4 of an hour.)

Answer. The Ling's speed on the second half of the distance was 6 mph.
               The average speed was 8 mph.


The solution by jorel555 is wrong in this part.
The error he made is TYPICAL and represents the good/classic example on how this problem SHOULD NOT be solved.