I need help please.

Laurie left home and ran to the lake at 10 mi/h. she ran back home at 8 mi/h. If the entire trip took 27 minutes, how far did she run in all?

the trip times are not the same, so the average speed is not 9 mph

sorry, Ms. Sue

why is it 9d/40??

Oops! Thanks for catching that, Scott.

I agree with Scott

time for first leg = d/10
time for return leg = d/8
total time = d/10 + d/8 = 9d/40

avg rate = total distance/total time
= 2d/(9d/40) = 2d(40/9d) = 80/9 mph

distance = (27/60)(80/9) = 4 miles
So she ran 4 miles in total.

check: 2 miles at 10 mph = 2/10 hrs
2 miles at 8 mph = 2/8 miles
total time = 2/10 + 2/8
= 1/5 + 1/4 = 9/20 hrs = 27 minutes.

To find the distance Laurie ran in total, we need to consider her speed and the time she spent running.

Let's assume the distance from her home to the lake is "d" miles.

We know Laurie's speed when she ran to the lake was 10 mi/h. So the time she spent running to the lake can be calculated using the formula: time = distance / speed. Therefore, the time taken to run to the lake is d / 10.

Similarly, when Laurie ran back home, her speed was 8 mi/h. So the time spent running back is d / 8.

Since the entire trip took 27 minutes, we can add up the times spent running to the lake and back to get the total time: d / 10 + d / 8 = 27/60 (convert 27 minutes to hours).

To solve for 'd', we can first simplify the equation by finding their common denominator (in this case, it is 40).

(8d + 10d) / (8 * 10) = 27/60

Simplifying further:

18d / 80 = 27/60

Cross-multiplying:

18d * 60 = 27 * 80

1080d = 2160

Dividing both sides by 1080:

d = 2160 / 1080

d = 2

So, the distance between Laurie's home and the lake is 2 miles.

To find the total distance she ran, we can simply add the distances traveled to and from the lake: 2 miles + 2 miles = 4 miles.

Therefore, Laurie ran a total distance of 4 miles.

d = r t ... t = d / r

27/60 = (d / 10) + (d / 8)

54/120 = (12 d / 120) + (15 d / 120)

d is the distance to the lake

She averaged 9 mph.

27 / 9 = 3 miles