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Grace and Brian Johnston and Caitlin Dickson were on a Christian volunteer mission to the small village of Ma'hanga.
Part of a 19-strong team from Bethlehem College in Tauranga, they were due to fly out on Saturday.
The accident occurred in heavy rain on Tuesday night NZ time. The van carrying the group reportedly lost control, rolled and ended up in a ditch. The Kenyan driver also died.
Bethlehem College principal Eoin Crosbie said: "This tragedy will touch the lives of many in this community as these were all wonderful people who served others first as part of their expression of their Christian faith."
Caitlin was a former student and two of the Johnstons' 10 children are still at the school.
Others from the Bethlehem College group were injured and are in hospital in Kisumu. Last night, a charge nurse told the Herald six NZ students and two adults were all stable, as were a number of Kenyans also hurt in the crash.
The three New Zealanders killed had visited Kenya before and were said to have been passionate about the work there, part of the college's mission partnership programme.
The tragedy happened while the group were returning to the Ark Quest School, in a village Mr Crosbie described as a "needy community".
Bethlehem has been in partnership with Ark Quest for more than two years and has similar links with the Solomon Islands and Tonga.
One of the injured students was Samuel McDougall. His aunt told the Herald he was in hospital with an injured shoulder, but "he's one of the lucky ones. His parents have spoken to him; he's fine, really."
She said the three deaths would send shockwaves through the tight-knit Bethlehem Christian community.
Also among the passengers were siblings Luke and Joy Fisher. Their parents Bill and Michele were meeting last night with Mr Crosbie.
Brian Johnston was a long-serving anaesthetist with the Bay of Plenty District Health Board.
Yesterday marked 26 years since he began work with the board. Chief executive Phil Cammish said Dr Johnston saw a need five years ago for an anaesthetist in Whakatane so travelled there each week.
"Brian was a dedicated Christian who is described by his colleagues as the nicest person you would ever meet, and someone who would only ever give, never take.
"Brian and Grace have also been described as being woven into the fabric of the Bay of Plenty and will be sorely missed."
In Kenya, Murang'a South traffic chief Loise Gatimu told local media most accidents in the region were caused by careless drivers.
"We are losing too many innocent lives on this road that has turned into a nightmare to residents due to careless driving. The rising carnage can only be checked if drivers observe traffic rules."
Friend Jim Cairns-Nelson, an anaesthetic technician, worked alongside Dr Johnston for almost 15 years and
is involved with the Otumoetai Eels Rugby League Club, where the Johnston boys Mike, Phil and Chris are players.
He said Dr and Mrs Johnston had 10 children and the family showed up regularly to watch the boys' matches.
"Brian was a real league man - he's a quiet man, but we used to talk Warriors all the time at the hospital."
Mr Cairns-Nelson said the Johnstons were "just the best kind of people, and parents you'd want your kids to be around".
Bethlehem's head of drama, Linda Anderson, said Caitlin Dickson got so much out of her experiences in Kenya last year that she had wanted to return. "She saw the opportunity and put her hand up."
Caitlin liked helping people so much that last year she shaved her head to raise money for the teenage cancer support charity CanTeen.
Tributes last night were posted on Facebook for the victims.
Laurence Matthew Dean wrote of Caitlin: "I refuse to believe that I will ever meet a woman with such a staggering zest for life as you. You loved unconditionally, your dorky sense of humour was infectious, you were everything we could have asked for and more ... I love you, Caitlin Dickson, always."
Krista Mortensen said Caitlin was a woman of amazing faith and love. "You are a legend, we love you."
- Andrew Koubaridis, Jamie Morton, Anna Leask and Vaimoana Tapaleao/additional reporting: Bay of Plenty Times