## toxicsugar22 5 years ago Andy drives 300 miles to Lake Tahoe at 70 miles per hour and returns home at 50 mph. What is his average speed for the round trip. (It is not 6o miles per hour.) Write expressions for the time it takes for each leg of the trip if Andy drives a distance d, at speed r base 1 and returns at speed r base 2

1. anonymous

Let the distance (of one way) be D the time taken to travel at 70 mph = D/70 the time taken to travel at 50 mph = D/50 total time taken = D/70 + D/50 ${D \over 70} + {D \over 50} = {50D + 70D \over (70)(50)} = {120D \over 3500} = {12D \over 350}$Total distance covered = D + D = 2D So, avg speed = ${2D \over { 120D / (70*50)}} = {3500*2 \over 120} = 58.33 mph$

2. anonymous

did you understand my process ?

3. toxicsugar22

yes

4. anonymous

There's another way to approach this problem which is by calculating the time spent in each trip and divide by the total distance traveled 300/70=x 300/50=y 600/(x+y) = 58.33

5. toxicsugar22

ok so what is the ime trip to Taoe

6. toxicsugar22

time

7. anonymous

the time trip TO taoe would be 300/70 = 4.29 hours

8. anonymous

so did yu understand everthing ?

9. toxicsugar22

ok and the time from trip home

10. anonymous

just like the way there: 300/50 = ?

11. toxicsugar22

ok i got it thanks