a The formula that relates distance to time is d=rt, or t= dr.
B
b Use the same formula as in Part A, but change the expression for rate.
C
c Sum up the time it takes Alicia to ride with the wind and against it.
D
d Use the results from Parts A, B, and C to solve for x, the speed of the wind.
A
a 20/11.5+x
B
b 20/11.5-x
C
c 3 hours 50 minutes
D
d 20/11.5+x+20/11.5-x=23/6; 3.5 mph
Practice makes perfect
a Alicia traveled 20 miles with the wind and 20 miles against it. The formula that relates distance to time is d=rt, or t= dr. Therefore, we can write the expression for Alicia's time with the wind as follows.
t=d/r ⇔ 20/11.5+x
b Because the rate will be slower when Alicia is biking against the wind, the expression for her time can be written as follows.
t=d/r ⇔ 20/11.5-x
c Alicia's total trip will be her biking with the wind and against it. Therefore, to find the total time we will sum up the time it takes her to bike with and against the wind.
Time with the wind+Time against the wind=Total time
⇕
1 hr 20 min+2 hr 30 min=3 hr 50 min
It will take Alicia 3 hours and 50 minutes, or 3 56 hours to complete the trip.
d The speed of the wind either increases or decreases the rate at which Alicia bikes. Therefore, the variable x in Part A and Part B represents the speed of the wind.
Time with the wind+Time against the wind=Total time
⇕
20/11.5+x+20/11.5-x=3 5/6
Let's solve this rational equation for x to determine the speed of the wind.
