Car A is traveling at 20 miles per hour Car B is one mile be

Car A is traveling at 20 miles per hour. Car B is one mile behind, following at 30 miles per hour. A fly can move 40 miles per hour. The fly begins on the front bumper of car B and flys back and forth between the two cars. How many miles will the fly travel before it is crushed in the collision?
Totally confused as to how to set it up. I know
Car A rate = 20/hr
Car B rate = 30/hr and distance = d-1
Fly rate hr

Solution

Car B is gaining on car A at 10 mph (30 - 20). To overtake car A 1 mile ahead at 10 mph will take 1/10 hours.
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The fly will go back and forth at 40 mph for 1/10 of an hour.
40*(1/10) = 4 miles.