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# Help

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A cyclist travels at 20 kilometers per hour when cycling uphill, 24 kilometers per hour when cycling on flat ground, and 30 kilometers per hour when cycling downhill. On a sunny day, they cycle the hilly road from Aopslandia to Beast Island before turning around and cycling back to Aopslandia. What was their average speed during the entire round trip?

Nov 3, 2019

#1
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Since the do an out and back trip....the up and down portions reverse and the flat remains the same

example:   on the way out   say    60 m up hill   = 3 hours

flat     48       = 2 hrs'

down  120    = 4 hrs

on the way back                           up 120          = 6 hrs

flat 48           = 2

down 60      = 2                          total miles 456 miles

total time = 19 hrs                 avg m/h = 456/19 = 24 m/hr

Nov 3, 2019
#2
+106539
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Thanks, EP......here's a general way of solving something like this

Assuming that  the road is uphill one way and downhill the other way....we have that....

Avg rate    =    Total Distance  / Total Time

Call the total  distance  =  2D

The total time is   ( D/ 30)  + (D /20)

So...we have that

Avg rate  =     ( 2D)                               2D                              2* 600

_____________  =       ______________  =       ______     =  24 mph

D/30 + D/24                D [ 30 + 20] /600                50

CORRECTED   !!!!

Nov 3, 2019
edited by CPhill  Nov 4, 2019
#3
+1

CPhill: Did you forget 20 km/h when cycling uphill?

Nov 3, 2019
#4
+106539
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Yep.....I realized later that I made an error ....since corrected!!!!...THX!!!!

CPhill  Nov 4, 2019