I read it as a kid in the 1980s but there is the possibility that it is an older book. I know the book was brand new when it was given to me. The main thing I remember about it was a story that was broken up into four or five parts interspersed with other stories or articles. The plot of the story concerned a rocket race in the solar system. Teams from various nations competed against each other; The US, Great Britain, Soviet Union, etc.. There was also artwork along with the story, I remember vividly the Soviet crew was depicted wearing uniforms with "CCCP" emblazoned on them, as was their rocket ship. I want to say that the US crew or the British crew ran into some trouble and had to rely on the other crew to help them out.
Possibly the series of six short stories by Clarke which were published collectively as 'Venture to the Moon'
"The Starting Line" tells of the launch of the first lunar expedition jointly by British, American and Russian rockets which have been assembled in Earth orbit. The plan is for all three ships to leave Earth orbit and land simultaneously, but the narrator has secretly been ordered to depart ahead of the other two ships. "Robin Hood FRS" tells of the efforts by the joint expedition members to recover an automatic supply rocket that has landed just out of reach, through the unorthodox method of utilising one team member's archery skills. "Green Fingers" describes how a Russian team member - a botanist - secretly engineers plant life that could survive on the Moon's surface, and the accident that causes his death. "All that Glitters" deals with a geophysicist who discovers diamonds on the moon - only to learn that back on Earth, synthetic diamonds have just been successfully created at negligible cost. "Watch this Space" tells how a scientific experiment conducted on the moon - creating a giant sodium cloud that is made luminescent by the sun's rays and visible from Earth - is sabotaged by "the greatest advertising coup" in history. "A Question of Residence" tells of how at the end of the mission one of the ships would have to stay behind to clean up their equipment while the others return and get the early glory, and how the British team end up volunteering... in order to take advantage of a legal loophole so they can sell their stories tax-free.
They are collected in 'The Other Side of the Sky', and were also published in illustrated form in the UK weekly comic Speed & Power