Intermath | Workshop Support


Freddy and Frieda

Problem Statement

| The Frog Race

Two frogs have a race. One frog makes a jump of 80 cm once every 5 seconds. The other frog makes a jump of 15 cm every 1 second. The rules of the race state that the frogs must cross a line 5 meters away and then return to the starting point. Which frog wins the race?

Problem setup

Two frogs are in a race. The frogs must cross the finish line which is 5 meters away. They then have to return to the starting point which means going 5 meters back. Freddy the Frog jumps 80 cm every 5 seconds on the clock. Frieda Frog jumps 15 cm every second on the clock. Who wins?


Plans to Solve/Investigate the Problem

First, I began thinking about the metric system in terms of meters, naturally, and a silver meter stick that I own. I began remembering my conversions such as 100 cm = 1 meter, 1000 mm = 1 meter. Those are the two that came to mind.


Investigation/Exploration of the Problem

In order to carry out this problem, I have to multiply 100 times 10 to get 1000 cm for the total race length in cm since they have to go 5 meters each way. I convert to cm since the problem gives me the length each frog jumps in the cm unit. If Freddy jumps 80 cm every 5 seconds, which means that he takes 62.5 seconds to finish the race. First, I divided 1000 by 80 which is 12.5. This tells me how many 5 second “chunks” he took to jump. Then, I multiply 12.5 by 5 and get 62.5 seconds or 1 minute and 2.5 seconds. Now for Frieda. Frieda jumps 15 cm every second. I take 1000 and divide it by 15 which equals 66.66. This means that Frieda uses 66.66 one second jumps for the race. So, I multiply 66.66 by 1 and get the same number, 66.66, of course. So in terms of minutes and seconds, Frieda uses 1 minute and 6.66 seconds to finish the race. Freddy wins! Poor Frieda…

Author & Contact
Pam Joseph



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