Sample Problem Solving Problem: Wildebeests

“It’s supposed to be spectacular! Why have we never been before?”

A heard of wildebeests decided that, since they were in Africa anyway, they might as well go see Victoria Falls. It took them two days to get there, during which they spent 21 hours traveling and covered a total of 123 miles. On the second day, they traveled 2 miles per hour faster than they did on the first day, but they also spent 3 fewer hours traveling on the second day than they did on the first. How many miles did the wildebeests travel on the second day?

To solve this problem, first determine how many hours the wildebeests traveled each day. If we let the number of hours they traveled on the second day be represented by t, then we can write:

hours traveled on the 1st day + hours traveled on the 2nd day = 21 total hours

hours traveled on the 1st day = t + 3

hours traveled on the 2nd day = t

(t + 3) +t = 21

2t + 3 = 21

2 t = 18

t = 9

So they spent 9 hours traveling the second day and 12 hours on the first day. 9 + 12 = 21, so that sounds right. Now we need to figure out how fast they went each day. Speed can be calculated with the following familiar formula:

speed = distance/time

This can be rearranged like so:

distance = speed(time)

We know how many hours they spent traveling each day and the total distance traveled, so if we let the speed on the first day be represented by s, then:

speed on the 1st day = s

speed on the 2nd day = s + 2

distance traveled on the 1st day = 12s

distance traveled on the second day = 9(s + 2)

distance traveled on the 1st day + distance traveled on the second day = 123 miles total

Ooo! Aaaahh!

12s + 9(s + 2) = 123

12s + 9s + 18 = 123

21s + 18 = 123

21s = 105

s = 5

So, the speed on the first day was 5 mph and the speed on the second day was 7 mph. To find the distance traveled on the second day, just take their speed on the second day times the time they spent traveling:

7(9) = 63

So the wildebeests traveled 63 miles on the second day.

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