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**+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

#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**+4 **

Best Answer

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