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"We thought it was sick at first, so we got close to it and we saw the tide was going out and it was beached," Allegretta told WA Today.
Video captured by the teenagers shows them working to keep the young dolphin calm while attempting to steer her out of the shallow waters.
"The mother wasn't anywhere around and the baby was doing its mimic call to attract her," Allegretta said.
"It was very stressed and very jumpy and obviously wasn't comfortable with the situation," he said. "As we came to it, it got more and more scared, and I started patting it so it calmed down."
"It took us about 30 minutes but we slowly got it into deeper water," Allegretta said. "Then its tail started going and it was off."
The video of the rescue ends with the dolphin calf swimming off into the distance.