+0

+3
48
3
+147

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?

joebob  Nov 4, 2017

#2
+78729
+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
Sort:

#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.

Guest Nov 4, 2017
#2
+78729
+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
+147
0

Thank you so much!

joebob  Nov 4, 2017

### 9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details