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?

His speed for remaining distance was___mph and his average speed was___mph.

so he biked 1 mile at 12 mph and the other 1 mile at x mph

1/12 + 1/x = 1/4 ---> 15 min = 1/4 hr
times 12x, (don't like fractions)
x + 12 = 3x
x = 6
so his speed for the second part was 6 mph

check:
time at 12 mph = 1/12 hr = 5 minute
time at 6 mph = 1/6 hr = 10 min
for a total of 15 min

Average speed = total distance/total time
= 2/(1/4) = 8 mph

do you notice that 8 is NOT the average of 12 and 6 ???

hi

To find Ling's speed for the remaining distance, we need to find the time it took him to cover the first half of the distance.

Since Ling lives 2 miles from school, and he biked the first half of the distance, he covered 1 mile.

Ling traveled at a speed of 12 mph for the first half of the distance and it took him 15 minutes.

We can use the formula for speed (speed = distance / time) to find the time it took him to cover 1 mile:

Speed = Distance / Time
12 mph = 1 mile / Time

Now, let's solve for Time:

Time = 1 mile / 12 mph
Time = 1/12 hour

Since Ling took 15 minutes to bike from school to home, which is equivalent to 1/4 hour, the time it took him to cover the first half of the distance is the remaining time:

Remaining Time = Total Time - Time for First Half
Remaining Time = 1/4 hour - 1/12 hour
Remaining Time = 3/12 hour - 1/12 hour
Remaining Time = 2/12 hour
Remaining Time = 1/6 hour

To find Ling's speed for the remaining distance, we use the formula for speed:

Speed = Distance / Time
Speed = 1 mile / (1/6 hour)
Speed = 6 miles per hour (mph)

Therefore, Ling's speed for the remaining distance was 6 mph.

To find the average speed, we use the formula:

Average Speed = Total Distance / Total Time
Average Speed = 2 miles / (1/4 hour)
Average Speed = 8 miles per hour (mph)

Therefore, Ling's average speed was 8 mph.

To find Ling's speed for the remaining distance, we need to know how long it took him to cover the first half of the distance.

We know that Ling took 15 minutes to bike from school to home, which covers a total distance of 2 miles. Since the first half of the distance is covered at a speed of 12 mph, we can say that Ling covered half the distance in distance/speed = time, or 1 mile / 12 mph = (1/12) hour.

Now, to find Ling's speed for the remaining distance, we need to know how long it took him to bike the second half of the distance. We can calculate this by subtracting the time taken for the first half from the total time.

Total time taken = 15 minutes = 15/60 = 1/4 hour
Time taken for the first half = 1/12 hour

Time taken for the second half = Total time taken - Time taken for the first half = (1/4) - (1/12) = (3/12) - (1/12) = 2/12 = 1/6 hour

Since we know the time taken for the second half and the distance traveled in the second half is 1 mile, we can calculate Ling's speed for the remaining distance.

Speed = Distance / Time = 1 mile / (1/6) hour = 6 miles per hour

Therefore, Ling's speed for the remaining distance was 6 mph.

To find Ling's average speed, we can use the formula:

Average speed = Total distance / Total time

Here, Ling traveled a total distance of 2 miles in a total time of 15 minutes or 1/4 hour.

Average speed = 2 miles / (1/4) hour = 8 miles per hour

Therefore, Ling's average speed was 8 mph.