Question

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?

Answer 1

May I help?

Answer 2

Sure :)

Answer 3

The average speed is the ratio of total distance traveled to the time consumed for walking this distance.

Answer 4

Which means:
the first distance equals speed times time (take care of units; they must be equivalent)
\[d_1=v.t=6*\frac{ 50 }{ 60 }=5 mile\]
for the second distance, it is the same

for the first time: it is 50 min =50/60 =5/6 hr
for the second time:
\[v_2=\frac{ x }{ t_2 }\]
\[12mph=\frac{ 5mile }{ t_2 }\]
\[t_2=\frac{ 5 }{ 12 }=0.41667hr\]


So that, the average speed will be
\[v_{aver}=\frac{ total distance }{ total time }=\frac{ 5+5 }{ \frac{ 5 }{ 6 }+\frac{ 5 }{ 12 } }=\frac{ 10 }{ \frac{ 5 }{ 4 } }=8mph\]

Answer 5

Sorry for being late!

Answer 6

Hope that helps

Answer 7

Thank you for the medal!