# Math: Speed and Distance

Topics: Speed, Miles per hour, Velocity Pages: 4 (848 words) Published: August 26, 2013
Karen Michelle L. Lim BSA – M6
Motion Problems:

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?  | Rate| Time| Distance|

Carlos| 12| n| 12n|
Denise| 36| 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.

2. 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?

| Rate| Time| Distance|
Boston to LA| 525| n + 2/3| 525n + 350|
Return trip| 600| n| 600n|

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.

3. 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 = 4tii) 45 - x = 3t + 3
We can substitute the...