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On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40 minutes longer to climb up than run down, what is the total length of Ted's hike?

Nov 4, 2017

#2
+99580
+4

Let D be 1/2 of the  Diistance

And 40 min  2/3 hr

So   using Distance / Rate  = Time in Hours .......we have that

D/3  =  D/5   + 2/3    simplify

D/3  +  [3D + 10] / 15     cross-multiply

15D  = 3[ 3D + 10]

15D  =  9D + 30     subtract 9D from both sides

6D  = 30   divide both sides by 6

D  = 5 miles

So...the total distance is twice this  =  10 miles

Nov 4, 2017

#1
+1

Let the time it takes to hike downhill =T

Distance = Speed x Time

5T =3(T+40), solve for T

5T = 3T + 120

5T - 3T = 120

2T = 120

T =120 / 2

T =60 - minutes, or 1 hour, to hike downhill.

Distance =1 x 5 mph=5 miles.

Nov 4, 2017
#2
+99580
+4

Let D be 1/2 of the  Diistance

And 40 min  2/3 hr

So   using Distance / Rate  = Time in Hours .......we have that

D/3  =  D/5   + 2/3    simplify

D/3  +  [3D + 10] / 15     cross-multiply

15D  = 3[ 3D + 10]

15D  =  9D + 30     subtract 9D from both sides

6D  = 30   divide both sides by 6

D  = 5 miles

So...the total distance is twice this  =  10 miles

CPhill Nov 4, 2017
#3
+205
+1

Thank you so much!

joebob  Nov 4, 2017