Answer:
a. 10v/(v² - 16) b. 3 hours
Explanation:
a. Write and simplify an equation for the amount of time t in hours it will take the cyclist to make the trip.
Let v be the speed of the cyclist without the wind. The speed of the cyclist with the 4 mile per hour wind in the direction of the wind is v' = v + 4. Since the distance travelled is 5 miles, and time, t = distance/speed, the time it takes to make this trip is t' = 5/(v + 4)
Let v be the speed of the cyclist. The speed of the cyclist with the 4 mile per hour wind against the direction of the wind is v" = v - 4. Since the distance travelled is 5 miles, and time, t = distance/speed, the time it takes to make this trip is t" = 5/(v - 4).
So, the total travel time, T = t' + t"
= 5/(v + 4) + 5/(v - 4)
= [5(v - 4) + 5(v + 4)]/[(v + 4)(v - 4)]
= [5v - 20 + 5v + 20)]/(v² - 4²)
= 10v/(v² - 16)
b. What is the cyclist's total travel time, if she travels an average of 6 miles per hour without the wind?
If v = 6 miles per hour, then
T = 10v/(v² - 16)
= 10(6)/(6² - 16)
= 60/(36 - 16)
= 60/20
= 3 hours