Problema Solution
Natasha rides her bike ( at a constant speed) for 4 hours, helped by a wind of 3 miles per hour. Pedaling the same rate, the trip back against the wind takes 10 hours. Find the round trip distance she traveled
Answer provided by our tutors
Let
v = Natasha's rate in still air, v>0
w = 3 mph the rate of the wind
d = the distance traveled in each direction
t1 = 4 hr the time of the trip with the wind
t2 = 10 hr the time of the trip against the wind
The speed of Natasha when traveling with the wind is: v + w = v + 3
The speed of Natasha when traveling against the wind is: v - w = v - 3
Since speed = distance/time we have:
v + 3 = d/t1
v + 3 = d/4
v - 3 = d/t2
v - 3 = d/10
By solving the system of equations:
v + 3 = d/4
v - 3 = d/10
........
........
d = 40 mi
The round trip distance is 2d = 2*40 = 80 miles in length.