Starting at home, Luis traveled uphill to the gift store for 50 minutes at just 6 mph. He then traveled back home along the same path downhill at a speed of 12 mph.
What is his average speed for the entire trip from home to the gift store and back?
Answers
Given:
(i) Starting at home, Luis traveled uphill to the gift store for 50 minutes at just 6 mph.
(ii) He then traveled back home along the same path downhill at a speed of 12 mph.
To find:
(i) The average speed of the entire trip
Solution:
We know that 1mph = 0.447m/s
So, 6mph = (6*0.447)m/s
= 2.682 m/s
Time taken to go uphill = 50mins = (50*60) = 3000s [1min = 60s]
So, distance travelled (D) = Speed*Time
= 2.682*3000 m
= 8046m
He travels this distance again while going back to home.
D = 8046m
S = 12mph = (12*0.447)m/s
= 5.364m/s
Time taken = D/S
= 8046/5.364 s
= 1500 s
So, total time taken in journey = (3000+1500)s
= 4500s
Total distance = 2(8046)m = 16092
Avg. speed = Distance/Time
= 16092/4500 m/s
= 3.576 m/s
= 3.576/0.447 mph
= 8 mph
So, the average speed is 8mph.