Mid-Chapter Quiz
Sign In
Use the d=rt formula. How many miles did Lucita travel at the faster pace?
Use the d=rt formula. At what pace did Lucita travel the second part of the distance?
Use the expressions from Part A and Part B.
50/x
50/x-15
100x-750/x(x-15)
Let x represent the faster pace in miles per hour. We know that Lucita traveled half the distance at this rate. Since the distance is 100 miles, she traveled 50 miles at rate x. Let's recall the formula for the distance d depending on the rate r and the time t.
d=rt
Lucita traveled the distance of 50 miles at the faster rate, x. Let's substitute these values into the formula above to find the time t_1 spent at the faster pace. t_1=50/x
We will use the formula from Part A for the time t depending on the distance d and the rate r.
We want to write an expression for the amount of time Lucita needs to complete the trip. In Part A we have found the time t_1 she spent at the faster pace. In Part B we have found the time t_2 she spent at the slower pace.
t_1 = 50/x t_2 = 50/x-15
The total time t of the trip is the time spent at the faster pace plus the time spent at the slower pace.
a/b=a * (x-15)/b * (x-15)
a/b=a * x/b * x
Distribute 50
It will take Lucita 100x-750x(x-15) hours to complete the trip.