Coelho is about halfway through his treatment and had been doing well. But a few days before the race, he developed a blood clot and was hospitalized.
When a text message from Coelho late Saturday promised he would be at the race, Smith said, "it was like a burst of energy."
With rock bands and cheer teams stationed throughout the course, the Rock 'n' Roll Half Marathon is part of a growing trend of fun, festival-atmosphere foot races.
But what makes the race, formerly called the Philadelphia Distance Run, a favorite among serious runners is the flat, fast, scenic course and a history of sunny but mild weather over its 36 years.
The course starts east from Eakins Oval, goes around City Hall and Independence Hall, back up the Parkway to Kelly Drive, across the Falls Bridge, and down to the finish line in front of the Art Museum.
The winners: Among men, Stanley Biwott, a 27-year-old Kenyan who won for the second year, finishing in 59 minutes, 36 seconds, and among the women, Lyudmyla Kovalenko, who set a Ukrainian record with a time of 1:08:59.
Thousands of people stuck around after the race to hear the Canadian rock band Walk Off the Earth.
Participants came from all 50 states and 19 countries.
For brothers Arnie and Adan Jaurez of Los Angeles, it was their first major race outside California.
They took the opportunity Saturday to explore City Hall, Independence Hall, and other spots. And of course, "we ran up the steps," Arnie Jaurez said, raising his arms in "Rocky" fashion.
Andy Berman of Moorestown marveled as the first elite runners passed by the Rodin Museum. "I don't know if, at a dead sprint, I could run this fast," he said.
"I could run like that for 100 miles," said his son Alex, 4. But asked if he could beat his mom, Caty, Alex was less confident.
"Not right now. But soon, probably," he said.
"She's on notice," his dad said.
At Logan Circle, runners cheered and sang along with Grateful Dead cover songs by local band Mother Zed.
"Our job is to give the runners some energy," said Rich Cohn, one of the band's frontmen.
It makes for a fun gig, Cohn said, even if their audience is constantly running away from them. "It's the biggest crowd we ever get, but only for 15 seconds."
Near the finish line, Courtney Brophy, 28, of Downingtown, was jumping frantically, shouting "Go, baby, go! Go, baby, go!"
Her husband, James Brophy, finished in 1:15:07. He shaved a couple of minutes off his goal and may have been in the first 100 finishers.
At the finish line around 9:30 a.m., coach Smith quickly spotted Coelho, holding a poster signed by the whole team.
Even before picking up a water bottle, Smith went over to hug him. They chatted for a moment, and Coelho said he was proud of what his coach had done - his first half marathon in nearly 15 years.
Then Coelho's mom leaned over the rail and wrapped her arms around the coach's neck.
BY THE NUMBERS
22,000 Number of runners who competed
59:36 Winning time in minutes and seconds
50 Number of states runners represented
19 Number of countries
Contact Jessica Parks at firstname.lastname@example.org, 610-313-8117, or follow on Twitter @ JS_Parks.