Algebra 1 Word Problem

Question

Three brothers participate in a 100m dash. When Allen finishes, Bernie has only completed 80m. When Bernie finished, Chuck had only completed 90m. The brothers would like to race again, so that all three of them will finish at the exact same time (assuming they run at the same speed as before). How far back do Allen and Bernie need to move back at the beginning of the race, so that they will finish when Chuck finishes his 100m?

Answer 1

The rates are such that distance traveled by C = 0.9 B and B = 0.8 A. Set C = 100 and work backwards to get B = 100/0.9 = 111.1 and A = 111.1/0.8 = 138.9 m. So Bernie needs to move back 11.1 m, and Allen needs to move back 38.9 m.