SOLUTION: Please help me! Starting at home, Jessica travelled uphill to the hardware store for 75 minutes at just 4 mph. She then travelled back home along the same path downhill at a sp

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Question 887023: Please help me!
Starting at home, Jessica travelled uphill to the hardware store for 75 minutes at just 4 mph. She then travelled back home along the same path downhill at a speed of 12 mph.
What is her average speed for the entire trip from home to the hardware store and back?
Found 3 solutions by josgarithmetic, MathTherapy, Alan3354:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Same distance d both ways.
RT=D rate time distance.

_______________rate________time_________distance
UP_____________4___________75%2F60__________d
DOWN__________12___________t______________d

Simplify the UP time hours and compute d:

_______________rate________time____________distance
UP_____________4___________1%261%2F4__________d=4(5/4)=5
DOWN__________12___________t_________________d=5

The time going DOWN can now easily be computed as t=5%2F12

Total distance is BOTH WAYS, up and down 5%2B5=10 miles.
Total time in hours is 5%2F4%2B5%2F12=15%2F12%2B5%2F12=20%2F12=5%2F3 hours.

Average Speed, 10%2F%285%2F3%29=%2810%2A3%29%2F5=highlight%286%29, miles per hour.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me!
Starting at home, Jessica travelled uphill to the hardware store for 75 minutes at just 4 mph. She then travelled back home along the same path downhill at a speed of 12 mph.
What is her average speed for the entire trip from home to the hardware store and back?


On uphill trip, distance traveled: %2875%2F60%29+%2A+4, or 5 miles

On downhill trip, time taken: 5%2F12 hr

Total distance: 2(5), or 10 miles

Total time: 75%2F60+%2B+5%2F12, or 15%2F12+%2B+5%2F12, or 20%2F12, or 5%2F3 hours



Average speed = total_distance%2Ftotal_time

Average speed = 10%2F%285%2F3%29______10+%2A+%283%2F5%29____2cross%2810%29+%2A+%283%2Fcross%285%29%29, or highlight_green%28highlight_green%286%29%29 mph

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Jessica travelled uphill to the hardware store at just 4 mph. She then travelled back home along the same path downhill at a speed of 12 mph.
---------
The distance does not matter.
Avg speed for a round trip is similar to parallel resistors.
Avg = 2*4*12/(4+12) = 6 mi/hr