Question

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?

Answer 1

Answer:

Step-by-step explanation:

Let

v1 = 12 mph

v2 = the speed of the second half

v = the average speed

t = 15 min = 15/60 hr = 1/4 hr = 0.25 hr

d = 2 mi

d/2 = 2/2 = 1 mi (half the distance)

Since speed = distance/time follows time = distance/speed:

(d/2)/v1 + (d/2)/v2 = t

1/12 + 1/v2 = 0.25

v2 = 6 mph

v = d/t

v = 2/0.25

v = 8 mph

The speed for the remaining distance is 6 mph.

The average speed for the whole trip is 8 mph.

Answer 2

Given data : 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.

To find : What was his speed for the remaining distance? What was his average speed ?

Solution : a/c to question;

• 15 minutes = 15/60 hour = 1/4 hour ( total time)

Now, we need to find the time taken by the ling to cover a distance of 1 mile at the speed of 12 mph.

⟹ speed = distance/time

⟹ 12 = 1/ time

⟹ time = 1/12 hour ----{1}

Now,

⟹ remaining time to cover 1 mile = total time - 1/12 hour

⟹ remaining time to cover 1 mile = 1/4 - 1/12

⟹ remaining time to cover 1 mile = 3/12 - 1/12

⟹ remaining time to cover 1 mile = 2/12

⟹ remaining time to cover 1 mile = 1/6 hour ----{2}

Now,

⟹ speed = distance/time

⟹ speed = 1/ 1/6

⟹ speed = 6 mph

Now, from eq. {1} and {2}

⟹ average speed = total distance/total time taken

⟹ average speed = (1 + 1)/(1/12 + 1/6)

⟹ average speed = 2/(1/12 + 2/12}

⟹ average speed = 2/ 3/12

⟹ average speed = 2/ 1/4

⟹ average speed = 2 * 4

⟹ average speed = 8 mph

Answer : Hence, the speed for the remaining distance of ling is 6 mph and average speed of ling us 8 mph.