2014-2015
MC 14 Solutions
Path and Perimeter
1.
A
B
2.
Erin would like to get to point B from point A. How many ways
are there to get from A to B if she can only stay on the dotted
lines and not walk over the same line more than once?
A
Three squares are joined together. The side of each square
measures 2 inches. What is the shortest path, in inches,
you can take from A to B following the dotted lines?
Answer:
4
______________
Answer:
8
______________
B
Use this picture to solve problems numbers 3 through 8.
Lizard Mountain Paths
B
6 mi
C 4 mi D
a) What is the shortest distance from point A to E?
A
3.
E
Answer:
Shortest: 17 mi
b) What is the longest distance from point A to E if you are visiting a point not more
than once?
4.
Serena traveled on path A-B-D-E on her bike, and she came back on path E-B-A. How
many miles did she travel?
5.
Vivian traveled on path A-C-D-E on her bike and came back to point A using the longest
path. How many miles did she travel?
6.
How many ways are there to get from point A to point E, if you can only visit a point
once? (Hint: list all possibilities in an organized way)
ABE, ABCDE, ABDE, ACBE, ACDE, ACBDE, ACDBE
7.
A biker is traveling from A to C to D to E. After half of the distance, he takes a break.
How much further, in miles does he have to travel?
8.
Maya, on her bike, is leaving Point A and wants to visit points B, C, D, and E, but not
necessarily in that order. What is the shortest distance that Maya can take if she has to
stay on the paths?
Longest: 27 mi
______________
Answer:
39 miles
______________
Answer:
45 miles
______________
Answer:
7 ways
______________
Answer:
9 miles
______________
Answer:
21 miles
______________
ACDBE : 6 + 4 + 4 + 7 = 21 miles
9.
A
B
C
D
Town A to town D is 24 miles. Town B to town C is 8 miles. If the distance from town C
to town D is half the distance from Town B to C, how many miles is it traveling from
Town A to C?
Answer:
20 miles
______________
2014-2015
10. A worm crawls around the outside of a square that is 15 feet on each
side. If his speed is one foot per minute, how many hour(s) will it
take the worm to crawl around the entire square?
Answer:
1 hour
15 ft
Since his speed is one foot per minutes, he will travel 15 feet in 15 minutes. The
distance around the entire square is 60 feet (15*4), so it will take him 60 minutes or
1 hour.
______________
11. If a train that is 1 ½ miles long takes 5 minutes to go through a crossing, how fast is the
train moving? Hint: how fast = speed; think about miles per hour.
Answer:
18 mph
60 minutes ÷ 5 = 12. There are 12 groups of 5 minutes in one hour. Think of how far the train will travel if
there are 12 groups of 5 minutes? 1.5 miles x 12 groups = 18 miles in one hour
______________
12. John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then
drove for another 3 hours at the rate of 55 mph to reach his destination. How many
miles did John drive?
Answer:
255 miles
______________
D = 45 * 2 + 3 * 55 = 255 miles.
13. Ayush walks along the edges of a rectangular pool from point A
to B to C to D, a distance of 38 meters. Aaron walks along the
edges of the same pool from B to C to D to A, a distance of 31
meters. What is the perimeter of the pool, in meters?
Together they cover a total of 3 lengths and 3 widths; since 38 +31 = 69
meters, we have:

3 lengths + 3 widths = 69

1 length + 1 width = 23

2 lengths + 2 widths (which is the perimeter) = 46 meters.
A
B
D
C
Answer:
46 meters
______________
14. Two cars started from the same point, at 5 am, traveling in opposite directions at 40
and 50 mph respectively. At what time will they be 450 miles apart?
Answer:
10 a.m.
After t hours the distances D1 and D2, in miles per hour, traveled by the two cars are given by
D1 = 40 t and D2 = 50 t
After t hours the distance D separating the two cars is given by: D = D1 + D2 = 40 t + 50 t = 90 t
Distance D will be equal to 450 miles when D = 90 t = 450 miles
To find the time t for D to be 450 miles, solve the above equation for t to obtain t = 5 hours.
5 am + 5 hours = 10 am
15. Sidhart travels from city A to city B to city C and back to city A. Each
city is 120 miles from the other two. His average rate from city A to
city B is 60 mph. His average rate from city B to city C is 40 mph. His
average rate from city C to city A is 24 mph. What is Sidhart’s
average rate for the entire trip, in miles per hour?
______________
Answer:
36 mph
______________
C
A
B
Divide the total distance traveled by the total time needed: 360 ÷ (2+3+5) = 36 mph.
Math Challenge 15 will be available online May 22, 2015 at www.mathinaction.org.