Karen Michelle L. Lim BSA – M6
1. Carlos begins jogging west at 12 km/hr at 10:00 A.M. Denise leaves the same place at 11:00 A.M. and bicycles at 36 km/hr toward Carlos. At what time of day will she overtake him?
| n - 1
| 36n - 36
Note: Denise travels one hour less than Carlos.
When Denise catches up, Carlos and Denise will have travelled equal distances.
12n = 36n - 36
-24n = -36
n = 1.5
Answer: Denise overtakes Carlos at 11:30 A.M.
It takes a plane 40 min. longer to fly from Boston to Los Angeles at 525 mph than it does to return at 600 mph. How far apart are the cities?
Boston to LA
| n + 2/3
| 525n + 350
Assume the flight paths are of equal length:
Distance from Boston to LA) = (Return trip distance)
525n + 350 = 600n
350 = 75n
14/3 = n
Using this value of n, we can compute the length of either trip:
Return trip = 600(14/3) = 2800 miles.
ANSWER: The cities are 2800 miles apart.
One hour after Yolanda started walking from X to Y, a distance of 45 miles; Bob started walking along the same road from Y to X. If Yolanda’s walking rate was 3 miles per hour and Bob’s was 4 miles per hour, how many miles has Bob walked when they met?
We can make a quick diagram of the problem.
One way to solve this problem is with a table. We want to know the distance Bob walked. The distance Bob walked is our variable. Let x = the distance Bob walked.
Together Yolanda and Bob walked 45 miles, so Yolanda walked 45 -x miles when they met. We are given the rate at which both of them walk. We are told Yolanda walked 1 more hour than Bob. If Bob walked t, Yolanda walked t + 1. The results are summarized in the table below.
We get two equations:
i) x = 4t
ii) 45 - x = 3t + 3
We can substitute the...
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