Each lap Matt cycles takes him 50 seconds. Each lap Dan cycles takes him 80 seconds. Dan and Matt start cycling at the same time at the start line. How many laps will they each have cycled when they are next at the start line together?

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Answer 1 · 2018-04-23T00:02:33

Matt will have traveled 8 laps
Dan will have traveled 5 laps.

Find the least common multiple of 50 and 80

Factors of 50 are 2 x 5 x 5
Factors of 80 are 2 x 2 x 2 x 2 x 5

eliminate one set of the common factors of 2 x 5 This leaves

LCM = # 2xx2 xx2 xx2 xx5 xx 5 = 400 #

For Matt this gives # 50 xx 8 = 400 # so 8 laps
For Dan this gives # 80 xx 5 = 400# so 5 laps.