Question

Math problem/ puzzle HELP

Two frogs are going to race. The racecourse is 100 feet up and 100 feet back. Kermit makes three jumps of 2 feet each in the same time it takes Freddy to make two jumps of 3 feet each. Who will win the race and by how much?

Answer 1

It takes x time for Kermit to make 3 jumps of 2 feet or for Freddy to make 2 jumps of 3 feet.

Kermit needs 50 jumps to get to the top, and another 50 jumps to get back.
That is 100 jumps altogether to cover the 200 ft.
\( 100 ~jumps \times \dfrac{x}{3~jumps} = 33 \dfrac{1}{3} x\)

Freddy makes a jump of 3 ft. In order to go 100 ft, he will overshoot the halfway point by 2 ft. On the way back, he starts 2 ft farther away than he needed to go, so Freddy really goes a total of 204 ft. Freddy will take a total of 68 jumps for the entire race.
\(68 ~jumps \times \dfrac{x}{2~jumps} = 34x\)

Kermit wins by \(\dfrac{2}{3}x \) time, or by 2/3 of the time it takes for him to make 3 jumps. Kermit wins by 4 ft.