+205
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?
+129852 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
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.
+129852 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
